A pilot flies her route in two straight-line segments. The displacement vector A for the first segment has a magnitude of 232 km and a direction 30.0o north of east. The displacement vector B for the second segment has a magnitude of 168 km and a direction due west. The resultant displacement vector is R = A + B and makes an angle θ with the direction due east. Using the component method, find (a) the magnitude of R and (b) the directional angle θ.

Answers

Answer 1

Answer:

a) 121 km

b) 74°

Explanation:

To start with, we assume that there exist two components, the East and the North. We'd be representing the East, by "e" and the North, by "n"

Now we start with the

First vector:

east1 = 232 cos 30 = 201

north1 = 232 sin 30 = 116

Now, that of the second vector will be

east 2 = - 168

north2 = 0

Next, we add the two together and get

East components

201 - 168 = 33 east

North components

116 + 0 = 116

Therefore, the magnitude has to be

magnitude = √(33² + 116²)

Magnitude = √14545

Magnitude = 121

tanθ = 116/33

Tanθ = 3.51

θ = tan^-1 3.51

θ = 74° North East


Related Questions

Starting from rest, a panther accelerates at 3 m/s/s for 10 seconds. What is the final velocity of the panther

Answers

Answer:

Final velocity = 30 m/s

Explanation:

We are given;

Initial velocity; u = 0 m/s

Acceleration; a = 3 m/s²

Time; t = 10 seconds

From Newton's first law of motion, the final velocity is given by the formula;

v = u + at

Plugging in the relevant values gives;

v = 0 + (3 × 10)

v = 30 m/s

Maddie Cat can ride her tricycle at an amazing speed of 3.75 meters per second.
How far can she go in 5.0 seconds?

Answers

Distance = (speed) x (time)

Distance = (3.75 m/s) x (5.0 s)

Distance = 18.75 meters

Answer: 3.75 x 5.0= 18.75 meters

Explanation:

What net force is needed to accelerate a 1.25 kg book 5.00 m/s2?

Answers

Answer:

F = 6.25 N

Explanation:

Given that,

Mass of the book is 1.25 kg

Acceleration of the book is 5 m/s²

We need to find the net force needed to accelerate the book. Net force is given by :

F = ma

[tex]F=1.25\times 5\\\\F=6.25\ N[/tex]

So, 6.25 N of force is acting on the book.

If an X-ray tube is operating at a current of 30.0 mA:a) How many electrons are striking the target per second? b) If the potential difference between the anode and cathode of this tube is 100.0 kV, how much power is expended

Answers

Answer:

Explanation:

A. Q= It

30E-3A=q

Ne = q

30E-3/1.6*10-19= N

N= 1.8*10^16 electrons

B. Power= I x v

= 30*10^-3A x 100*10^3v

= 3000watts

What is the magnitude of total charge of all the electrons in 1.2 L of liquid water?

Answers

Answer:

6.416*10^ 8C

Explanation:

First we find mass of the water

Mass= density x volume

=1.2*1000= 1200g

To find number of moles we use

N= mass/ molar mass

= 1200/18.02= 66.6mol

So the total number of water molecules is

66.6* 6.022*10^23= 401.07x 10^23moles

But each h20 moles has 10 electrons so it will be 4.01*10^26electrons

Then finally total charge will be

4.01*10^26electrons x 1.6*10^-19

= 6.416*10^ 8C

The magnitude of total charge will be "6.416×10⁸ C".

Electrons:

According to the question,

Density, d = 1.2 L

Volume, V = 1000

The mass will be:

→ Mass = Density × Volume

By substituting the values,

            = [tex]1.2\times 1000[/tex]

            = [tex]1200[/tex] g

Now,

The number of moles will be:

→ N = [tex]\frac{Mass}{Molar \ mass}[/tex]

      = [tex]\frac{1200}{18.02}[/tex]

      = [tex]66.6[/tex] mol

The total no. of water molecules be:

= [tex]66.6\times 6.022\times 10^{23}[/tex]

= [tex]401.07\times 10^{23}[/tex] moles

hence,

The total charge be:

= [tex]4.01\times 10^{26}\times 1.6\times 10^{-19}[/tex]

= [tex]6.416\times 10^8[/tex] C

Thus the above response is correct.

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Explain why a golf ball has a higher density than a ping pong ball, even though they are similar in size and shape.

Answers

Answer:

The ping pong ball is hollow.

Explanation:

Since a ping pong ball, unlike the golf ball, is only filled with air, it is less dense. Air is notably LESS dense than solids, which is what comprises the inside of a golf ball.

Tony completed a 720 km journey with an average speed of 90 km/h for the first 285 km he travelled at an average speed of 95 Km/h what was the average speed for the remaining journey

Answers

Answer:

[tex]Speed = 87 km/h[/tex]

Explanation:

Given

Total Distance = 720km

Average Speed = 90km/h

Average Speed (285km) = 95km/h

Required

Determine the average speed for the rest of the journey

First we need to determine the time taken to complete the journey using

[tex]Speed = \frac{Distance}{Time}[/tex]

[tex]90 = \frac{720}{Time_1}[/tex]

Make Time the subject of formula

[tex]Time_1 = \frac{720}{90}[/tex]

[tex]Time_1 = 8 hour[/tex]

Next, we determine the time taken to complete 285km of the journey using

[tex]Speed = \frac{Distance}{Time}[/tex]

[tex]95 = \frac{285}{Time_2}[/tex]

Make Time the subject of formula

[tex]Time_2 = \frac{285}{95}[/tex]

[tex]Time_2 = 3 hours[/tex]

The difference between these calculated times is the time taken to complete the rest of the journey

[tex]Time = Time_1 - Time_2[/tex]

[tex]Time = 8\ hour - 3\ hour[/tex]

[tex]Time = 5\ hour[/tex]

Also, we need to calculate the distance of the rest of the journey

[tex]Distance = 720\ km - 285\ km[/tex]

[tex]Distance = 435\ km[/tex]

The average speed can then be calculated;

[tex]Speed = \frac{Distance}{Time}[/tex]

[tex]Speed = \frac{435}{5}[/tex]

[tex]Speed = 87 km/h[/tex]

Hence, the average speed of the rest of the journey is 87km/h

If a gannet hits the water at 32 m/s, what height did it dive from? Assume that the gannet was motionless before starting its dive.

Answers

Answer:

The value  is  [tex]h =  52.2 \  m[/tex]

Explanation:

From the question we are told that

 The  velocity  at which he hit the water  is  [tex]v  =  32 \  m/s[/tex]

   

Generally from kinematic equation

     [tex]v^2 =  u^2  + 2gh[/tex]

Here the initial velocity u = 0 m/   given that the gannet started the jump from rest.

  =>   [tex]32^2  =  0^2  +  2*(9.8)h[/tex]

 =>     [tex]h =  52.2 \  m[/tex]

a) An electric circuit is rates, 240V, 13Ω calculate the amount of current that can be used by this appliance.​

Answers

Answer:

18.4615385 amps

Explanation:

The voltage V in volts (V) is equal to the current I in amps (A) times the resistance R in ohms (Ω):

Which is the most dense solid?

Answers

Answer:

Bolt

Explanation:

The bolt is the most dense solid.

A container weighs 450 lb when filled with 4 ft3 of fluid. If the empty container weighs 50 lb, determine the specific weight, mass density and specific gravity of this fluid.

Answers

Answer:

112.5 lb/ft³

405.93 kg/m³

0.406

Explanation:

given that

Weight of the container, w(c) = 450 lb

Volume of fluid, v(f) = 4 ft³

Weight of empty container, w(e) = 50 lb

Specific weight is said to be the weight per unit volume. Thus, the specific weight of this fluid is

w(s) = 450 / 4

w(s) = 112.5 lb/ft³

Mass density is the ratio of the mass of the fluid, with respect to the volume.

ρ = m/v

Since the question gives us the mass in weight, we'd have to convert it to mass from weight.

mass = weight / acceleration due to gravity

mass = 450 / 9.81

mass = 45.87 kg

Also, since the mass is going to be in kg, the volume also has to be in m³, thus needing a conversion.

4 ft³ = 0.113 m³

Mass density = 45.87 / 0.113

Mass density = 405.93 kg/m³

Specific gravity of the fluid is simply given as mass density / 1000. Therefore,

g(s) = 405.93 / 1000

g(s) = 0.406

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Two vectors of magnitudes |A| = 8 units and |B| = 5 units make an angle that can vary from 0° to 180°. The magnitude of the resultant vector A + B CANNOT have the value of:

Answers

The question is missing the alternatives. Here is the complete question.

Two vectors of magnitude |A| = 8units and |B| = 5units make an angle that can vary from 0° to 180°. The magnitude of the resultant vector A+B CANNOT have the value of:

A. 2 units

B. 5 units

C. 8 units

D. 12 units

Answer: A. 2 units

Explanation: Vector is an entity that has characteristics as magnitude and direction. Resultant vector is the "sum" of 2 or more vectors.

In this question, the vectors have magnitude and angle varies from 0° to 180°.

When angle between vectors A and B is 0°, they are parallel and pointing to the same direction, so:

[tex]V_{R} = |A| + |B|[/tex]

[tex]V_{R}=8+5[/tex]

[tex]V_{R}[/tex] = 13

When the angle is 180°, it means vectors are in opposing directions, so:

[tex]V_{R} = |A| - |B|[/tex]

[tex]V_{R} = 8-5[/tex]

[tex]V_{R}[/tex] = 3

From the calculations, we can conclude the magnitude of resultant vector varies between 3 and 13.

The least value is 3, so it cannot have a value of 2 units.

How does society shape reality?

Answers

Society shapes us through our gender, it dictates what jobs would be suitable for us, what we should wear, how we should look, who we are to socialise with and what is acceptable or not.

A particle makes 240 revolutions per minute on a circle of radius 2m. Find I. its period ii. angular velocity III. linear velocity.​

Answers

Answer:

(i) The period, T is 0.25 s

(ii) The angular velocity, ω is 25.136 rad/s

(iii) The linear velocity is, v is 50.27 m/s

Explanation:

Given;

number of revolution of the particle, N = 240 revolutions per minutes

radius of the circle, R = 2m

(i) The period is given by;

[tex]T = \frac{2\pi}{\omega}[/tex]

where;

ω is angular velocity  

[tex]\omega = (240 \frac{rev}{min}) *(\frac{1 \ min}{60 \ s} )*(2\pi \frac{rad}{rev})\\\\ \omega = 25.136 \ rad/s[/tex]

[tex]T = \frac{2\pi }{\omega}\\\\ T = \frac{2\pi}{25.136}\\\\T = 0.25 \ s[/tex]

(ii) angular velocity, ω  = 25.136 rad/s

(iii) linear velocity is given by;

v = ωR

v = (25.136 rad/s) x (2 m)

v = 50.27 m/s

If you do not have enough time to complete a full workout, you should:
A. Cut the cool-down portion short.
B. Skip the warm-up and cool-down portions altogether.
C. Cut the warm-up portion short.
D. Cut the exercise portion short.

Answers

Answer:

the answer to this question would be cut the exercise portion down (D)

this is because warm ups and cooling down during exercise are more important than the exercise itself

Explanation:

A person with a black belt in taekwondo has a foot with a mass of 0.90 kg. Starting from rest, this foot attains a velocity of 8.3 m/s in 0.13 s. What is the magnitude of the average net force applied to the foot to obtain that acceleration?

Answers

Answer:

57.42 N

Explanation:

We first find the acceleration knowing that it goes from rest to 8.3 m/s in 0.13 seconds,

Therefore, the acceleration is:

[tex]a=\frac{v_f-v_i}{time} =\frac{8.3-0}{0.13 } =63.8\,\,m/s^2[/tex]

Now we use this to calculate the average net force by multiplying mass times acceleration:

F = m * a = 0.9 (63.8) = 57.42 N

Which is true for a car moving around a circular track with constant speed? 1. It has zero acceleration2. it has an acceleration directed toward the center of its path3. it has an acceleration directed away fromt he center of its path4. it has an acceleration with a direction that cannot be determined from the information given5. it has an acceleration component in the direction of its velocity.

Answers

Answer:

2. it has an acceleration directed toward the center of its path

Explanation:

For a car moving with constant velocity around a circular track, there is a a change in the direction of the velocity at every point on the path taken by the car around the track. This change in direction generates an acceleration on the car which will be directed towards the center of the track. This is why the inertia force on a person inside the car when it is driven around a circular track is usually away from the center of the track, since the inertia force acts in an opposite direction to the acceleration on a body.

assume this car is driven off a cliff. How many arrows of force need to be drawn in the free body diagram? Assum no air resistance

Answers:
five
one
four
three

Answers

Answer:

4

Explanation:

friction

weight

normal reaction

force to overcome inertia

Answer:

1

Explanation:

--->

Trevor and Nick are taxi drivers. Trevor drives a taxi using diesel oil while Nick drives a taxi using LPG. Whose taxi will cause higher levels of air pollution and why?

Answers

Answer:

Trevor's taxi would cause higher levels of air pollution

Explanation:

Trevor's taxi use diesel oil.

Diesel is less cleaner than LPG.

Compared to automotive pollution from petrol and diesel, pollutants from LPG-driven cars include lower amounts of petroleum hydrocarbons, nitrogen oxides , sulphur oxides, ozone contamination and particulate matter.

Please help!
A tennis ball falls off a shelf and bounces several times. Each bounce is lower than the one before. Soon the ball stops. Why doesn’t the ball keep bouncing?

A) some of the energy is changed into mass

B) The energy becomes stored in the ball

C) Energy is transferred to the air and ground

Answers

Answer:

c

Explanation:

energy isn't stored and it doesn't change to mass

The ball has some kinetic energy when it hits the floor, but some of it is changed, so it loses some of it each time it bounces. After a few bounces, the ball has so little kinetic energy remaining that it stops bouncing. Thus, option C is correct.

What doesn’t the ball keep bouncing?

Since the gravitational potential energy, which can be transformed back into kinetic energy on the rebound, increases with the drop height, the consequent bounce height will likewise rise.

Because it has the most elasticity, the rubber ball will rebound the highest when all three balls are dropped from the same height. Because rubber is incredibly elastic, it squishes or compresses as it touches the ground but immediately snaps back to its original shape.

Therefore, Additionally, some energy is changed into other forms like heat and sound. The majority of these additional energy sources are lost and not recovered, causing the ball to bounce back to a lesser height.

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Would a human feel more gravity on a bigger planet or less gravity

Answers

Answer: you would feel more gravity

Explanation: the more mass of an object the more pull

A flag pole is attached to the side of a building 5.00 ft off the ground and it hangs down 30 degrees from the vertical. If the pole is 6.00 ft in length, how high in feet is the top of the pole at its highest point (sticking out from building)? (Hint: draw a picture) E​

Answers

Answer:

   h ’= 0.6963 m

this is the height of the part of the post it supports.

Explanation:

For this exercise we can use the trigonometric relationships

Let's start by finding the vertical component of the height of the pole

             cos 30 = x / L

             x = L cos 30

             x = 6 cps 30

             x = 5.196 m

with this length, the post has the same height as the building, so there are

               Aₓ = L -x

               Δx = 6 -5.196

               Δx = 0.804 ft

the height of this section is

               cos 30 = h ’/ Dx

               h ’= 0.804 cos30

               h ’= 0.6963 m

this is the height of the part of the post it supports.

The fastest land animal is the cheetah. A cheetah can run 100 meter dash in 5.95 seconds, calculate the cheetahs average speed in meters per second

Answers

Answer:

16.80672269 m/s

Explanation:

100 divide by 5.95 seconds

Answer:

16.8m/s

Explanation:

S=D/T

=

[tex] \frac{100}{5.95} [/tex]

=16.80672269

=16.8

What is the equation of the line on the graph?

Answers

Position = (4 m/s)(time) +5

What two processes are involved in the formation of Earth’s magnetic field?

Answers

Answer:

i. Geodynamo

ii. Gravitational energy conversion

Explanation:

The outer core of the Earth is believed to be in molten form, consisting of mainly iron and nickel. The reaction (mixture) between these components or elements generates conventional currents which is maintained by the gravitational energy produced in the process. Thus, magnetic fields are generated continuously due to the continuous flow of electric current during the processes.

How does the Coriolis effect impact ocean currents in the Northern and Southern Hemispheres?

Answers

The Coriolis effect describes the pattern of deflection taken by objects not firmly connected to the ground as they travel long distances around the Earth.The key to the Coriolis effect lies in Earth’s rotation. Specifically, Earth rotates faster at the Equator than it does at the poles. Earth is wider at the Equator, sThe Coriolis effect bends the direction of surface currents to the right in the Northern Hemisphere and left in the Southern Hemisphere.

Let’s pretend you’re standing at the Equator and you want to throw a ball to your friend in the middle of North America. If you throw the ball in a straight line, it will appear to land to the right of your friend because he’s moving slower and has not caught up.

 

Now let’s pretend you’re standing at the North Pole. When you throw the ball to your friend, it will again to appear to land to the right of him. But this time, it’s because he’s moving faster than you are and has moved ahead of the ball.

Everywhere you play global-scale "catch" in the Northern Hemisphere, the ball will deflect to the right.

To practice Problem-Solving Strategy 22.1 for electric force problems. Two charged particles, with charges q1=qq1=q and q2=4qq2=4q, are located on the x axis separated by a distance of 2.00cm2.00cm . A third charged particle, with charge q3=qq3=q, is placed on the x axis such that the magnitude of the force that charge 1 exerts on charge 3 is equal to the force that charge 2 exerts on charge 3.Find the position of charge 3 when qqq = 2.00 nCnC .

Answers

Answer:

x₂ = 0.01336

Explanation:

In this exercise we use the translational equilibrium equation

          F₁₃ - F₂₃ = 0

          F₁₃ = F₂₃

at the point where charge 3 is placed the two electric forces have the same magnitude

let us use the expression of Coulomb's law for the electric force

         F₁₃ = ka q₁ q₃ / r₁₃²

         F₂₃ = ka q₂ q₃ / r₂₃²

we substitute

         k q₁ q₃ / r₁₃² = k q₂ q₃ / r₂₃²

now imprescriptibility suppose that particle 1 is at the origin of the coordinate system, particle 2 is at a distance d = 2.00cm = 2 10-2 m, therefore let's call the distance from particle 1 to particle 3 as x

            r₁₃ = x

            R₂₃ = d-x

In the exercise we are given the charges for the particle1 q1 = q, for the particle 2 the charge is q2 = 4q the distance between them is d = 2.00cm = 0.0200 m, the value of q = 2.00 nC = 2.00 10⁻⁹ C

let's substitute these values

              q₁ / x₂ = q₂ / (d-x)²

let's clear x

              (d-x)² = q₂ / q₁    x²

              d² - 2dx + x₂ = q₂ /q₁   x²

               x² (1-q₂ / q₁) - 2d x + d² = 0

               

let's substitute the values ​​and solve the quadratic equation

              x² (1 - 4q / q) - 2 0.02 x + 0.02² = 0

              -3 x² - 0.04 x + 0.0004 = 0

               

                x² + 0.0133 x - 0.0001333 = 0

               x = [-0.0133 ±√(0.0133² + 4 0.00013333)] / 2

                x = [-0.0133 + - 0.026664] /2

              x₁ = -0.01998 m

              x₂ = 0.01336 m

Since load 3 must be between charged 1 and 2 the correct answer is

x₂ = 0.01336

If you want to replicate another scientist's experiment, which sections of their laboratory report will provide you with the most valuable information?

Answers

If research results can be replicated, it means they are more likely to be correct. Replication is important in science so scientists can “check their work.” The result of an investigation is not likely to be well accepted unless the investigation is repeated many times and the same result is always obtained.

How does diet affect diabetes

Answers

Answer:

A diet high in fat, calories, and cholesterol increases your risk of diabetes. A poor diet can lead to obesity (another risk factor for diabetes) and other health problems. A healthy diet is high in fiber and low in fat, cholesterol, salt, and sugar. Also, remember to watch your portion size.

Lower sugar levels for you have a healthier diet

Can an objects displacement be greater than or equal to the objects distance?

Answers

If you say displacement is greater than distance, you will contradict the above statement. Displacement is always less than or equal to distance. Note that distance is a scalar whereas displacement is a vector.So' displacement cannot be more than distance.
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