a)The velocity of the second runner relative to the first will be 0.8 m/s.
b)The second runner will win.
c) The distance ahead will the winner be when she crosses the finish line will be 55.6 m.
What is velocity?The change of distance with respect to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.
Given data;
The relative distance between the runner, S = 45.0 m.
The velocity of the front runner,v₁ = 3.45 m/s
The velocity of the second runner,v₂ = 4.25 m/s,
The distance of front runners from the finish line =250 m
The velocity of the second runner relative to the first is,v₂₁=?
The first runner's time to cross the finish line is,t₁
The second runner's time to cross the finish line is recorded,t₂
The distance ahead will the winner be when she crosses the finish line is, S₂₁
a)
The velocity of the second runner relative to the first is found as;
v₂₁ = v₂-v₁
v₂₁ =4.25-3.45
v₂₁ = 0.8 m/s in the runners' direction of travel.
b)
The first runner's time to cross the finish line is;
t₁ = 250/3.45
t₁=72.5 secs.
The second runner's time to cross the finish line is recorded;
t₂=(250+45)/4.25
t₂=69.4 secs.
So, the winner is the second runner.
c)
The winner will be in front when she crosses the finish line by a distance, The second runner travels a distance of within this time.
S₂ = 250+45
S₂=295 m.
The distance ahead will the winner be when she crosses the finish line is;
S₂₁ = 295-239.4
S₂₁=55.6
Hence, the velocity of the second runner relative to the first will be 0.8 m/s, the second runner will win. and the distance ahead will the winner be when she crosses the finish line will be 55.6 m.
To learn more about the velocity, refer to the link: https://brainly.com/question/862972
#SPJ1
A set of four capacitors are attached to a 12V battery in the circuit shown below. All capacitances are measured in milli-Farads. Find the amount of electric charge that resides on each capacitor once it is fully charged.
The amount of electric charge that resides on each capacitor once it is fully charged is 0.37 C.
Total capacitance of the circuit
The total capacitance of the circuit is calculated as follows;
Capacitors in series;
1/Ct = 1/8 + 1/7.5
1/Ct = 0.25833
Ct = 3.87 mF
Capacitors is parallel;
Ct = 3.87 mF + 12 mF + 15 mF
Ct = 30.87 mF
Ct = 0.03087 F
Charge in each capacitorQ = CV
Q = 0.03087 x 12
Q = 0.37 C
Thus, the amount of electric charge that resides on each capacitor once it is fully charged is 0.37 C.
Learn more about capacitors here: https://brainly.com/question/13578522
#SPJ1
How does the increasing mass effect the force of an object in motion?
Answer:
According to second law of motion,the acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased.
So simply, it can be affected due to increasing force as there is close relationship between momentum.
Explanation:
The more inertia that an object has, the more mass that it has. A more massive object has a greater tendency to resist changes in its state of motion.
I hope it was helpful for you :)
A 10.0 Ω lightbulb is connected to a 12.0 V battery. (a) What current flows through the bulb? (b) What is the power of the bulb?
The current flowing through the bulb as well the power of the bulb are 1.2A and 14.4 Watts respectively.
What current flows through the bulb as well as the power of the bulb?From ohm's law; V = I × R
Where V is the voltage, I is the current and R is the resistance.
Also, Power is expressed as; P = V × I
Where V is voltage and I is current.
Given that;
Resistance R = 10.0 ohmsVoltage V = 12.0VCurrent I = ?Power P = ?First, we determine the current flow through the bulb.
V = I × R
12.0V = I × 10.0 ohms
I = 12.0 ÷ 10.0
I = 1.2A
Next, we determine the power of the bulb.
P = V × I
P = 12.0V × 1.2A
P = 14.4 Watts
Therefore, the current flowing through the bulb as well the power of the bulb are 1.2A and 14.4 Watts respectively.
Learn more about Ohm's law here: brainly.com/question/12948166
#SPJ1
A plank of length L=2.200 m and mass M=4.00 kg is suspended horizontally by a thin cable at one end and to a pivot on a wall at the other end as shown. The cable is attached at a height H=1.70 m above the pivot and the plank's CM is located a distance d=0.700 m from the pivot.
Calculate the tension in the cable.
The tension in the cable is 23.2 N
What is the tension in the string?The tension in the cable can be resolved into horizontal and vertical forces Tcosθ and Tsinθ respectively.
Tcosθ, is acting perpendicularly, Tcosθ = 0
Taking moments about the pivot:
Tsinθ * 2.2 = 4 * 9.8 * 0.7
Solving for θ;
θ = tan⁻¹(1.4/2.2) = 32.5°
T = 27.44/(sin 32.5 * 2.2)
T = 23.2 N
In conclusion, the tension in the cable is determined by taking moments about the pivot.
Learn more about moments of forces at: https://brainly.com/question/23826701
#SPJ1
What is the power of a motor that transfers 550 J of energy in 11s?
Answer:
The answer is 50 watts
Explanation:
The formula of power is work done over elapsed time
P= W/t
P= 550 J / 11 sec
P= 50 watts
An object with a mass of m = 3.85 kg is suspended at rest between the ceiling and the floor by two thin vertical ropes.
The magnitude of the tension in the lower rope is 12.8 N. Calculate the magnitude of the tension in the upper rope.
24.93 N is incorrect.
The tension in the upper rope is determined as 50.53 N.
Tension in the upper rope
The tension in the upper rope is calculated as follows;
T(u) = T(d)+ mg
where;
T(u) is tension in upper ropeT(d) is tension in lower ropeT(u) = 12.8 N + 3.85(9.8)
T(u) = 50.53 N
Thus, the tension in the upper rope is determined as 50.53 N.
Learn more about tension here: https://brainly.com/question/918617
#SPJ1
An object, whose mass is 0.660 kg, is attached to a spring with a force constant of 132 N/m. The object rests upon a frictionless, horizontal surface (shown in the figure below).
An object labeled m is attached to the right end of a horizontal spring, and the left end of the spring is attached to a wall. The spring is stretched horizontally such that the object is displaced by a distance A to the right of its equilibrium position.
The object is pulled to the right a distance A = 0.120 m from its equilibrium position (the vertical dashed line) and held motionless. The object is then released from rest.
(a)
At the instant of release, what is the magnitude of the spring force (in N) acting upon the object?
N
(b)
At that very instant, what is the magnitude of the object's acceleration (in m/s2)?
m/s2
(c)
In what direction does the acceleration vector point at the instant of release?
Toward the equilibrium position (i.e., to the left in the figure).
Away from the equilibrium position (i.e., to the right in the figure).
The direction is not defined (i.e., the acceleration is zero).
You cannot tell without more information.
Answer:
See below
Explanation:
a) Spring force at release = k * d = 132 N/m * .120 m = 15.84 N
b) F = ma
15.84 = (.660 kg)(a) a = 24 m/s^2
c) Toward the left ....the object is accelerated to the left
A. The magnitude of the spring force acting upon the object at the instant of release is approximately 15.84 N.
B. With the moment of release, the object is moving with an acceleration of about [tex]\rm -24 m/s^2[/tex].
C. The correct option is toward the equilibrium position (i.e., to the left in the figure).
Let us calculate the magnitude of the spring force, the acceleration of the object and the direction of the vector at the time of release.
Given:
Mass of the object (m) = 0.660 kg
Force constant of the spring (k) = 132 N/m
Displacement from equilibrium (x) = 0.120 m
Magnitude of the spring force [tex]\rm (F_s_p_r_i_n_g):[/tex]
To determine the spring force at the time of release, we can apply Hooke's law. According to Hooke's law, the force of a spring depends on how far it has moved from its equilibrium position. Hooke's law is expressed as:
[tex]\rm F_s_p_r_i_n_g[/tex] = -k * x
where
[tex]\rm F_s_p_r_i_n_g[/tex] is the spring force,
k is the force constant of the spring, and
x is the displacement from the equilibrium position.
When we put the values, we get:
[tex]\rm F_s_p_r_i_n_g[/tex] = -132 N/m * 0.120 m
[tex]\rm F_s_p_r_i_n_g[/tex] = -15.84 N
Therefore, the magnitude of the spring force acting upon the object at the instant of release is approximately 15.84 N.
The net force acting on the object at the time of release determines its acceleration. The spring force and any additional external forces acting on the object add up to form the net force. In this case the spring force is the only force acting on the object.
According to Newton's second law of motion, the acceleration of an object is inversely related to its mass and directly proportional to the total force exerted on it. Acceleration is calculated as:
a = [tex]\rm F_n_e_t[/tex] / m
where
a is the acceleration,
[tex]\rm F_n_e_t[/tex] is the net force, and
m is the mass of the object.
Noting that the mass (M) is 0.660 kg and the net force (-15.84 N) is equal to the force of the spring, we can plug the following numbers into the formula:
a = (-15.84 N) / 0.660 kg
a = [tex]\rm -24 m/s^2[/tex]
Therefore, with the moment of release, the object is moving with an acceleration of about [tex]\rm -24 m/s^2[/tex].
The direction of the acceleration vector is left in the diagram, or towards the equilibrium position. This is because the negative sign of the acceleration value indicates that the acceleration is moving in the direction opposite to that in which the equilibrium position has moved. Since the signal indicates that the object first moved to the right, acceleration will be applied to the left in an attempt to bring the object back to its equilibrium position.
So, the correct option is toward the equilibrium position (i.e., to the left in the figure).
Learn more about Acceleration, here:
https://brainly.com/question/2303856
#SPJ3
Question 9 of 27
While working out, a man performed 500 J of work in 8 seconds. What was
his power?
The power of man performing 500 J of work in 8 seconds is 62.5 J/s.
Power can be defined as the pace at which work is completed in a given amount of time.
Horsepower is sometimes used to describe the power of motor vehicles and other machinery.
The pace at which work is done on an item is defined as its power. Power is a temporal quantity.
Which is connected to how quickly a project is completed.
The power formula is shown below.
Power = Energy / Time
Power = E / T
Because the standard metric unit for labour is the Joule and the standard metric unit for time is the second, the standard metric unit for power is a Joule / second, defined as a Watt and abbreviated W.
Here we have given Energy as 500 J and Time as 8 second.
Power = Energy / Time
Power = 500 / 8 Joule / sec
Power = 250 / 4 Joule / sec
Power = 125 / 2 Joule / sec
Power = 62.5 Joule / sec or 62.5 watt
Power came out to be 62.5 J/s when the man performed 500 Joule of work in 8 seconds.
So we can conclude that the power in the Energy transmitted per unit of time, and can be find out by dividing Energy by time. In our case the Power came out to be 62.5 Joule / Second.
Learn more about Power here:
https://brainly.com/question/1634438
#SPJ10
How is Behaviorism and Psychoanalysis theories are similar and different?
How do i solve for the point of equigravity between two planets, given their mass ratio and the distance between them ?
The equigravity between two planets is determined from the product and their masses and square of distance between them.
Gravitational force between two planetsThe gravitational force between two planets is calculated as follows;
F = GM₁M₂/R²
where;
G is universal gravitation constantM₁ is mass of first planetM₂ is mass of the second planetR is the distance between the two planetsUse the mass ratio of the two planets to determine their individual masses.
Thus, the equigravity between two planets is determined from the product and their masses and square of distance between them.
Learn more about gravitational force here: https://brainly.com/question/72250
#SPJ1
A surveyor measures the distance across a straight river by the following method: Starting directly across from a tree on the opposite bank, he walks x = 112 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline to the tree is = 37.8°.
How wide is the river?
y = _____________ m
y = 11.3380m
What is Young's double-slit experiment?The double-slit experiment is an experiment, that shows that light has both a wave nature or characteristic and a particle nature or characteristic, and that these natures are inseparable.
So, light is said to have wave–particle duality rather than be only a wave or only a particle. The same is true for electrons and other quantum particles.
According to the question,
The relative to angle θ, its adjacent side has length x and its opposite side is equal to width of the river, y;
tanθ = [tex]\frac{y}{d}[/tex] = y = dtanθ
y =( 112m) tan (37.8° )
y ≈ 11.3380m
The width of river is 11.3380m
Learn more about Young's double-slit experiment here:
https://brainly.com/question/17167388
#SPJ1
Lesson 2 History of Physical Science
Write an expository essay explaining how science builds on itself. Use at least two specific examples from this lesson.
Science builds on itself because the process of science is iterative and not predetermined.
How do science builds on itself?Science is said to build on itself because the process of science is iterative. This means that science does not have a linear path but circles back on itself so that useful ideas are built upon and used to learn even more about the natural world.
For instance, the discovery of inheritance that could be passed from parent to their offspring by Gregor Mendel.
Many more scientist has worked subsequently on chromosome, gene and DNA.
They have continued to deepen and extend our understanding of genes, how they are controlled, how patterns of control themselves are inherited, and how they produce the physical traits that pass from generation to generation.
Science is said to build on itself because the process of science is not predetermined. This means that carrying out an experiment on an idea would lead to the discovery of a new idea altogether.
Learn more about science here:
https://brainly.com/question/17216882
#SPJ1
A rocket uses 400.0 J of chemical potential energy stored in the fuel while shooting the 0.55 kg rocket straight up
into the air. The rocket reaches a height of 23 m. What was the efficiency of the rocket in transforming the chemical
potential energy of the fuel into gravitational potential energy?
Select one:
O a. 25%
Ob. 35%
O c. 31%
O d. 29%
Answer:
Approximately [tex]31\%[/tex] assuming that [tex]g = 9.81\; {\rm N \cdot kg^{-1}}[/tex].
Explanation:
Consider an object of mass [tex]m[/tex] in a uniform gravitational field of strength [tex]g[/tex]. If the height of that object increased by [tex]\Delta h[/tex], the gravitational potential energy of that object would increase by [tex]m\, g\, \Delta h[/tex].
In this question, the mass of the rocket is given to be [tex]m = 0.55\; {\rm kg}[/tex]. Assume that [tex]g = 9.81\; {\rm N \cdot kg^{-1}}[/tex]. The rocket has gained a height of [tex]\Delta h = 23\; {\rm m}[/tex]. Thus, the gravitational potential energy of this rocket would have increased by:
[tex]\begin{aligned} m\, g\, \Delta h &= 0.55\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \times 23\; {\rm m} \\ &\approx 124.1\; {\rm J} \end{aligned}[/tex].
In other words, the useful energy output from the combustion of the rocket fuel was approximately [tex]124.1\; {\rm J}[/tex].
The energy input to this rocket was given to be [tex]400.0\; {\rm J}[/tex]. Thus, the efficiency of the energy conversion would be:
[tex]\begin{aligned} \text{efficiency} &= \frac{(\text{useful energy out}\text{put})}{(\text{energy in}\text{put})} \times 100\% \\ &\approx \frac{124.1\; {\rm J}}{400.0\; {\rm J}} \times 100\% \\ &\approx 31\%\end{aligned}[/tex].
Set local ground level to 700 ft, and record the inches of mercury.
What is the altimeter reading in inches of mercury (from the Kollsman window)?
The main way in which an altimeter measures the altitude of an object is by calculating the location's air pressure.
What is an Altimeter?This refers to the instrument that is used to measure the altitude of an object when it is at a fixed level.
Hence, we can see that an altimeter should NOT be confused with a barometer, because although they both measure pressure, a barometer calculates the change in air pressure and elevation based on available weather.
Please note that your question is incomplete so I gave you a general overview to help you get a better understanding of the concept.
Read more about altimeters here:
https://brainly.com/question/17633815
#SPJ1
Question:- A planet X moves in an elliptical path as shown below. At which point does the planet moves faster. Assume, Ethiopian institute of space science and technology, allows to launch a space station with you. While you are in orbit, you gets thirsty. The only thing in the space station were a cup of water. you go to the cup of water and pick it up,But unfortunately your hand is twisted and the cup is turned down.Because the cup is turned down, water pour on to the floor.How would you get water?
We can get water from the sweat and exhaled breath of the people present in the space station.
How would you get water?We can get water from the sweat and exhaled breath. The water we drink is recycled from the sweat and exhaled breath of the people present in the space station which was collected through condensation on the Space Station's walls.
So we can conclude we can get water from the sweat and exhaled breath of the people present in the space station.
Learn more about water here: https://brainly.com/question/1313076
#SPJ1
A car drives 16 miles south and then 12 miles west. What is the magnitude of the car's displacement?
O4 miles
16 miles
20 miles
28 miles
Answer:
20 miles
Explanation:
Use pythagorean theorem
d^2 = 16^2 + 12^2
to find displacement, d = 20 miles
I need help with this question, could you help me? :))) ASAP
Many years ago, a scientist discovered an animal P and studied its characteristics. Some of the characteristics of animal P are as follows:
A Lays egg
B has four legs
C Can swim in the water
D Can produce milk to feed the young.
Which of the above characteristics made it difficult to classify animal P as a mammal?
Answer:
A
Explanation:
most mammals are viviparous instead of oviparous. oviparous means laying eggs
Calculate the work done by pulling an object through a distance of 30metres by a force of 220 newton
Answer:
6600J
Explanation:
the formula for work is: W= F x d
F- force, d- distance
How is Behaviorism and Psychoanalysis theories are similar?
Answer:
One of the key similarities between both the psychoanalytical theory and the behavioral theory is that both are by and large, deterministic.
The larger the mass of a star, the higher the internal pressures. Higher internal pressures causes higher temperatures and it is temperature that determines the types of fusion that can occur deep in a stars interior. Discuss the types of fusion that can occur in a star, the temperatures at which they occur, and the mass required to produce them.
The types of fusion that occurs in stars are:
proton-proton fusion - stars with temperatures less than 15 million Kelvin and masses of 0.08 solar mass or more.carbon cycle fusion - occurs in stars with temperatures of 15 million Kelvin or more and masses of 4.0 solar mass or morehelium fusion - occurs in stars with temperatures of 100 million Kelvin or more and masses of 0.5 solar mass or moreWhat is a nuclear fusion reaction?A nuclear fusion is reaction in which nucleus of small atoms combine together to produces atoms of larger nucleus.
The types of nuclear fusion that can occur in a star include;
Proton-proton fusion - occur in stars with core temperatures less than 15 million Kelvin and masses of 0.08 solar mass or more.Carbon cycle fusion occurs in stars with core temperatures greater than 15 million Kelvin having masses of 4.0 solar mass or more.Helium fusion - occurs in stars with core temperatures greater than 100 million Kelvin and masses of 0.5 solar mass or moreIn conclusion, the types of fusion that occur in stars are proton-proton fusion, carbon cycle fusion and helium fusion.
Learn more about nuclear fusion at: https://brainly.com/question/982293
#SPJ1
A house is advertised as having 1580 square feet under roof. What is the area of this house in square meters?
The area of the house will be 146.78 in square meters
What we have given in the question is that there is one house whose area is measured in square feet which is 1580 square feet, and we have to convert that area in square meter.
Now, To convert the area in square meter we must divide the area given in square feet by a constant which is 10.764.
Area in square meter = Area in square feet / 10.764
Area in square meter = 1580 / 10.764 square meter
Area in square meter = 146.78 square mete
Thus we conclude that You must divide the area given in square feet by 10.764 to convert Square feet to Square meters and vice versa for the opposite and after calculation we found that area which is 1580 square feet will be 146.78 in magnitude in square meters
Learn more about Area Calculation here:
https://brainly.com/question/23422101
#SPJ10
FRICTION INVESTIGATION
Summarize your findings in a short report of 150 words. Include your hypothesis, observations, data, calculations, and conclusion. The answers to the questions below should be included in your conclusion.
Why didn't the box slide off the table before you put enough coins in the bag?
What was the coefficient for the smooth surface? For the rough surface?
What was the difference between the two coefficients? What caused this difference?
What factors caused a margin for human error in this investigation?
Would the coefficient vary if you tied the string to a similar object of different masses, but on the same surface? Explain.
What did you learn from this investigation? Be thoughtful in your answer.
Based on the nature of friction:
the box did not slide off the table before you put enough coins in the bag due to friction.The coefficient of the friction of the rough surface is greater than that of the smooth surfaceThe difference is due to the nature of the surfaces.Human errors could occur if the coins are not added carefullythe coefficient of friction is a constant for a given surface and independent of the mass of the object.What is friction?Friction is the opposition to the relative motion of an object over another at their surfaces of contact.
The coefficient of friction is a ratio of the frictional force and the normal reaction.
Coefficient of friction = frictional force/normal reactionThe coefficient of friction of rough surfaces is greater than that of smooth surfaces.
In the given experiment:
the box did not slide off the table before you put enough coins in the bag because of friction between the box and the tableThe coefficient of the friction of the rough surface is greater than the coefficient of friction of the smooth surfaceThe difference between the two values of coefficient of friction is due to the nature of the surfaces.Human errors in the experiment could occur when the coins are not added carefullyThe coefficient of friction of each surface is constant and independent of the massIn conclusion, the experiment demonstrates that the coefficient of friction is a constant for given surfaces and does not depend on the mass of the object.
Learn more about coefficient of friction at: https://brainly.com/question/10907027
#SPJ1
You have two rocks made of the same material that are at the same
temperature. The first rock has twice the mass of the second rock. How does
the thermal energy of the two rocks compare?
A. The second rock has four times the thermal energy of the second
rock.
B. The first rock has half as much thermal energy as the second rock.
OC. The rocks have the same amount of thermal energy.
D. The first rock has twice as much thermal energy as the second
rock.
Answer:
I think its C
Answer:
D
Explanation:
If the temperature doesn't change but the mass of the object increases, the thermal energy in the object increases.
What is resistance force?
A. The force opposing the effort
B. The force exerted by the machine
C. The work put into a machine
D. A force that improved on your effort?
Answer asap
Answer:
A
Explanation:
resisting is doing something that goes against what something or someone is doing therefore the resisting force is the opposing force
A 12.0 μF capacitor is charged to a potential of 50.0 V and then discharged through a 265 Ω resistor. A)How long does the capacitor take to loose half its charge?
B) How long does it take the capacitor to loose half of its stored energy?
(a) The time for the capacitor to loose half its charge is 2.2 ms.
(b) The time for the capacitor to loose half its energy is 1.59 ms.
Time taken to loose half of its charge
q(t) = q₀e-^(t/RC)
q(t)/q₀ = e-^(t/RC)
0.5q₀/q₀ = e-^(t/RC)
0.5 = e-^(t/RC)
1/2 = e-^(t/RC)
t/RC = ln(2)
t = RC x ln(2)
t = (12 x 10⁻⁶ x 265) x ln(2)
t = 2.2 x 10⁻³ s
t = 2.2 ms
Time taken to loose half of its stored energyU(t) = Ue-^(t/RC)
U = ¹/₂Q²/C
(Ue-^(t/RC))²/2C = Q₀²/2Ce
e^(2t/RC) = e
2t/RC = 1
t = RC/2
t = (265 x 12 x 10⁻⁶)/2
t = 1.59 x 10⁻³ s
t = 1.59 ms
Thus, the time for the capacitor to loose half its charge is 2.2 ms and the time for the capacitor to loose half its energy is 1.59 ms.
Learn more about energy stored in capacitor here: https://brainly.com/question/14811408
#SPJ1
A supersonic airplane is flying horizontally at a speed of 2610 km/h.
1. What is the centripetal acceleration of the airplane, if it turns from North to East on a circular path with a radius of 80.5 km?
2. How much time does the turn take?
3. How much distance does the airplane cover during the turn?
Answer:
Centripetal acceleration of this aircraft: approximately [tex]6.52\; {\rm m \cdot s^{-2}}[/tex].
Distance covered during the turn: approximately [tex]63.2\; {\rm km}[/tex].
Time required for the turn: approximately [tex]0.0242\; \text{hours}[/tex] (approximately [tex]87.2\; {\rm s}[/tex].)
Explanation:
Convert velocity and radius to standard units:
[tex]\begin{aligned}v &= 2610\; {\rm km \cdot h^{-1}} \times \frac{1\; {\rm h}}{3600\; {\rm s}} \times \frac{1000\; {\rm m}}{1\; {\rm km}} \\ &= 725\; {\rm m\cdot s^{-1}} \end{aligned}[/tex].
[tex]\begin{aligned} r = 80.5\; {\rm km} \times \frac{1000\; {\rm m}}{1\; {\rm km}} = 8.05 \times 10^{4}\; {\rm m}\end{aligned}[/tex].
Hence, the centripetal acceleration of this aircraft:
[tex]\begin{aligned} a &= \frac{v^{2}}{r} \\ &= \frac{(725\; {\rm m\cdot s^{-1}})^{2} }{8.05 \times 10^{4}\; {\rm m}} \\ &\approx 6.53\; {\rm m \cdot s^{-2}}\end{aligned}[/tex].
The trajectory of the turn is an arc with a radius of [tex]r = 80.5\; {\rm km}[/tex] and a central angle of [tex]\theta = 90^{\circ} = (\pi / 4)[/tex]. The length of this arc would be:
[tex]\begin{aligned} s &= r\, \theta \\ &= 80.5\; {\rm km} \times (\pi / 4) \\ &\approx 63.2\; {\rm km}\end{aligned}[/tex].
The time required to travel [tex]63.2\; {\rm km}[/tex] at a speed of [tex]2610\; {\rm km \cdot h^{-1}}[/tex] would be:
[tex]\begin{aligned}t &= \frac{s}{v} \\ &\approx \frac{63.2\; {\rm km}}{2610\; {\rm km \cdot h^{-1}}} \\ &\approx 0.0242\; {\rm h} \\ &\approx 0.0242 \; {\rm h} \times \frac{3600\; {\rm s}}{1\; {\rm h}} \\ &\approx 87.2\; {\rm s} \end{aligned}[/tex].
A watermelon is blown into three pieces by a large firecracker. Two pieces of equal mass m fly away perpendicular to one another, one in the x direction another in the y direction. Both of these pieces fly away with a speed of V = 23 m/s. The third piece has three times the mass of the other two pieces.
Write an expression for the speed of the larger piece, that is in terms of only the variable V.
What is the numeric value for the speed of the larger piece, in meters per second?
At what angle does the largest piece travel with respect to the -y axis, in degrees?
(a) The expression for the speed of the larger piece is [tex]\frac{v\sqrt{2} }{3}[/tex].
(b) The numeric value for the speed of the larger piece is 10.84 m/s.
(c) The direction of the larger piece is 45⁰ with respect to y - axis.
Expression for the speed of the larger piece
Apply the principle of conservation of linear momentum;
m₁v₁ + m₂v₂ + m₃v₃ = 0
where;
m₁ is mass of first piecem₂ is mass of second piecem₃ is mass of third piece = three times the mass of other piece = 3mmv.i + mv.j + (3m)v₃ = 0
(3m)v₃ = -mv.i - mv.j
3v₃ = - v.i - v.j
[tex]v_3 = \frac{-v_i \ - \ v_j}{3} = \frac{v\ (\sqrt{(-1)^2 + (-1)^2} )}{3} = \frac{v\ \sqrt{2} }{3}[/tex]
Numeric value for the speed of the larger piece[tex]v_3 = \frac{23 \times \sqrt{2} }{3} \\\\v_3 = 10.84 \ m/s[/tex]
Direction of the larger piecetan θ = vj/vi
tan θ = 1/1
tan θ = 1
θ = arc tan(1)
θ = 45⁰
Learn more about linear momentum here: https://brainly.com/question/7538238
#SPJ1
A device that uses electricity and magnetism to create motion is called a
Answer:
electric motors is the answer
A force F parallel to X-axis is starching a very light horizontal spring. Variation of force F vs. X, elongation of the spring is shown in the figure. (a)What is the spring force constant? (b) Calculate the work done by the force F as the spring elongates from x=4.0 cm to x=8.0 m.
The spring constant is obtained from the ratio of applied force to the elongation of the spring. The work done by the force is 2F.
Spring constant
The spring constant is obtained from the ratio of applied force to the elongation of the spring.
k = F/x (N/m)
Work done by the forceThe work done by the force is calculated as follows;
W = ¹/₂FΔx
where;
F is applied forceΔx is elongation of the spring = 8 m - 4 m = 4 mW = ¹/₂F(4)
W = 2F
Thus, the spring constant is obtained from the ratio of applied force to the elongation of the spring. The work done by the force is 2F.
Learn more about spring constant here: https://brainly.com/question/1968517
#SPJ1