module 1 question 13

At the end of a race a runner decelerates from a velocity of 9.00 m/s at a rate of 0.400 m/s2.
(a) How far does she travel in the next 14.0 s?
m
(b) What is her final velocity?
m/s

Answer:

It produces grooves and lands.

The resultant vector is middle line which is the longest line representing the single effect of the two vectors at both ends.

A resultant vector is defined as a single vector that produces the same effect as the two or more vectors combined together.

A resultant vector is usually, drawn to join the head of the first vector to the tail of the second in a triangle method of vector addition.

Also, a resultant vector can be determined by applying parallelogram law of vector addition.

Mathematically, a resultant vector can be determined using this formula,

R² = a² + b² - 2ab cosθ

where;

A resultant vector is always bigger than the two vectors acting together.

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The magnitude of the horizontal component of the balls initial velocity if the angle between the horizontal and the direction of the 5.0 meters per second decreases from 30 degrees to 20 degrees is 4.7 m / s

cos θ = Adjacent side / Hypotenuse

θ = 20°

V = 5 m / s

Since the direction of ball makes a right angled triangle with the horizontal,

cos θ = [tex]V_{x}[/tex] / V

[tex]V_{x}[/tex] = cos 20° * 5

[tex]V_{x}[/tex] = 0.94 * 5

[tex]V_{x}[/tex] = 4.7 m / s

The formula used to solve is called as trigonometric ratios formulas. The basic formulae are:

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

Therefore, the magnitude of the horizontal component of the balls initial velocity is 4.7 m / s

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The value of the iguana’s northward displacement is 1 meter.

The velocity V of iguana is 10m/s.

The time for which iguana runs is 5 seconds.

The angle it is making with the north is 30°.

The velocity of iguana will have two components now,

One along east and one along north.

The component along east is Vcos(30°).

And the component along north is Vsin(30°).

The horizontal displacement of the iguana is,

Northward displacement = northward velocity × time.

The northward velocity is 10sin(30°).

Time is 5 seconds no matter where the iguana moves.

So,

Northwards displacement = 10sin(30°)/5

Northwards displacement = 10/10 = 1m

The displacement in north is 1 meter.

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Answer:

See below

Explanation:

Is that 600 WATT lamp ?   If so:

   power =  I V

      600 w   =  2 A   * v

       v = 300 v

The tension in the rope and  the smallest value the angle θ can have if the rope is not to break

This is further explained below.

Generally, the equation for the tension  is mathematically given as

[tex]2 T sin \theta = m g[/tex]

Therefore

2*T*sin(11.1) = 87.6 * 9.81

T=2232 N

the tension in the rope is T=2232 N

b)

Generally, the equation for the angle is mathematically given as

[tex]2*2.55E4*sin \theta = 87.6*9.81[/tex]

Therefore

[tex]\theta = arcsin( \frac{87.6*9.81}{(2*2.55E4))}[/tex]

[tex]\theta=0.966 \textdegree[/tex]

In conclusion, The smallest value the angle θ can have if the rope is not to break is

[tex]\theta=0.966 \textdegree[/tex]

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Given

v = 343 m/s

ac = 5g

ac = 5*9.8 m/s^2

ac = 49 m/s^2

where,

v: velocity

ac = centripetal aceleration

Procedure

We call the acceleration of an object moving in uniform circular motion—resulting from a net external force—the centripetal acceleration ac; centripetal means “toward the center” or “center seeking”.

Formula

The minimum radius not to exceed the centripetal acceleration is 2401 m.

      The rate at which an object's velocity with respect to time changes is referred to as acceleration in mechanics. It is a vector quantity to accelerate (in that they have magnitude and direction). The direction of the net force applied on the item determines the object's acceleration.

        The definition of acceleration (symbol: a) in physics or physical science is the rate of change (or derivative with respect to time) of velocity.

       The equation a = v/t denotes acceleration (a), which is the change in velocity (v) over the change in time (t).

     The displacement that an object or particle experiences with respect to time is expressed vectorially as velocity. The meter per second (m/s) is the accepted unit of velocity magnitude (also known as speed).

         When an item is travelling at a constant speed, its acceleration can be zero. There won't be any acceleration because the speed is constant, hence there won't be any change in speed. Zero acceleration is shown by the graph above.

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x and y directions are the component of projectile motion. x represents horizontal motion and y represents vertical motion.

There are the two components of the projectile motion - horizontal and vertical movement. And on the grounds that perpendicular components of movement are impartial of every other, these  components of movement can be mentioned separately.

Projectile motion is a form of movement skilled by an object or particle that is projected close to Earth's surface and moves alongside a curved route under the action of gravity most effective.

Projectile motion is the movement of an item thrown into the air. After the preliminary pressure that launches the item, it only experiences the pressure of gravity. The item is known as a projectile, and its route is known as its trajectory.

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In the diagram the numbered parts are:

1. Muscle belly

2. Fascicle

3. Epimysium

4. Myofibril

5. Muscle fiber

6. Endomysium

7. single muscle fiber

8. H zone

9. Z disc

10. Sarcolemma

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Mass does not affect the speed of falling objects, As there is only gravity acting on them.

The mass of Uranus exists: 8.681 × 10²⁵kg

The radius of Uranus exists: 15,759.2 miles

Acceleration due to gravity exists as the acceleration gained by an object due to gravitational force.

Its SI unit exists m/s2. It contains both magnitude and direction.

The planet would be a space probe with a mass of 250Kg

The distance is 25m.

Mass does not affect the speed of falling objects, As there is only gravity acting on them.

The mass of Uranus exists m = 8.681 × 10²⁵kg

The radius of Uranus exists: 15,759.2 miles

Therefore, the correct answer is option D. Uranus

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The acceleration of the boat is 2.8 m/s².

Acceleration is the fee of trade of the rate of an object with admire to time. Accelerations are vector quantities. The orientation of an item's acceleration is given by means of the orientation of the internet pressure appearing on that object.

The acceleration is the rate of change of displacement. Acceleration is the price of an alternative to speed. velocity is a vector amount as it consists of each magnitude and path. Acceleration is also a vector amount as it's far just the rate of alternate speed. Newton s 2nd law of movement additionally referred to as the law of force and Acceleration, a pressure upon an item causes it to accelerate consistent with the method internet force = mass x acceleration.

So the acceleration of the object is at once proportional to the pressure and inversely proportional to the mass.

Calculation:-

v = u - at

8 = 22 - a×5

a = (22 - 8)/5

a = 2.8 m/s²

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Any mass greater than 150g attached to 100g will make the block move towards point A. Thus, there can be any number of blocks attached to it, but the total mass of the attached blocks must add up to 150g.

The newton, abbreviated N, is the SI unit of force. These are base units that are pertinent to force.

The symbol for the length unit of a meter is m. the kilogram (kg), a unit of mass. s stands for the second, a unit of time.

Seesaws are regulated by a straightforward equation that states that for balance to occur, the force applied to one end of the seesaw multiplied by the distance from the pivot should equal the force applied to the other side of the seesaw multiplied by the distance from the pivot.

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Answer:

One of the first things we need to know is the mass of the astronaut and equipment combined. Weight is given by the formula:

W = m x g, where m is the mass of the object(kg) and g is the gravitational acceleration on Earth's surface(9.8 m/s^2)

Knowing the weight of the astronaut and equipment, we get:

m = W / g

m = 2,156 N / 9.8 m/s^2 ( ^2 represents the power of 2)

m = 219.9 kg

Now, one last thing we need to know is the resulting velocity of the astronaut in the opposite direction. Once the astronaut throws the wrench from their equipment, according to the 3rd law of motion, the astronaut and the wrench will move in opposite directions because the astronaut pushed the wrench, and in return, the astronaut is pushed by the wrench. Having all these, we need to work with momentum.

p = m * v, where p is the object's momentum, m is mass and v is its velocity

let's call [tex]m_{a}[/tex] the astronaut's mass(combined with their equipment, including the wrench since it's initially part of the equipment)

[tex]m_{w}[/tex] = 5.0 kg is the wrench's mass

[tex]v_{wrench}{[/tex] = 5.0 m/s is the wrench velocity after it was thrown

The astronaut's momentum(before the thrown wrench): [tex]p_{before}=m_{a} * 0 = 0[/tex], because the astronaut's initial velocity is zero(including the equipment and wrench)

The astronaut threw the wrench. Therefore, we get the following momentum: [tex]p_{after} = m_{w} * v_{wrench} + (m_{a} - m_{w} ) * v_{after}[/tex]

The reason why we subtract the astronaut and equipment mass from the wrench's mass is that the astronaut and the equipment move independently from the wrench, therefore we exclude the wrench's mass.

The 3rd law of motion also implies that the total momentum of a system of objects interacting(colliding against one another) doesn't change. Therefore:

[tex]p_{before} = p_{after}[/tex]

Plugging all the values, we get:

5.0 kg * 5.0 m/s + (219.9 kg - 5.0 kg) * [tex]v_{after}[/tex] = 0

Solving the above equation, we get that the resulting velocity of the astronaut in the opposite direction is:

[tex]v_{after}=-8.596 m/s[/tex]

Note: The minus denotes the opposite direction the astronaut has after it was pushed by the wrench.

From the information given, the forces are

F1 = −78i + 44j

F2 = 87i + 80j

We would apply the dot product.

F1F2 = <- 78, 44> * <87i, 80j>

F1F2 = - 78(87) + 44(80) = - 6786 + 3520

F1F2 = - 3266

|F1| = √[(- 78)^2 + 44^2] = √8020

|F2| = √[87^2 + 80^2] = √13969

The angle between them is

θ = Cos^-1[F1F2/(|F1||F2|)

θ = Cos^-1(- 3266/√8020 * √13969

θ = Cos^-1(- 0.30856)

θ = 108 degrees

the angle between the cables is 108 degrees

The car is going at speed of 3.82 m/s at the end of the breaking period and the car traveled the distance from the start is 25.33 m.

The rate of change in an object's velocity concerning time is known as acceleration in mechanics. The vector quantity of accelerations. The direction of the net force that is acting on an object determines its acceleration.

Since acceleration has both a magnitude and a direction, it is a vector quantity. Velocity is a vector quantity as well. The definition of acceleration is the change in velocity vector over a time interval divided by the time interval.

According to the question, the given values are :

Time, t₁ = 4.9 s

Time, t₂ = 1.60 s

Acceleration, a₁ = 1.4 m/s²

Acceleration, a₂ = -1.9 m/s²

Initial Velocity, u = 0 m/s

(a)

By the Equation of motion,

v = u + a₁t₁

v = 0 + (1.4)(4.9)

v = 6.86 m/s.

Now, the velocity of the car at the end of the breaking period :

v' = v + a₂t₂

v' = 6.86 + (-1.9)(1.60)

v' = 3.82 m/s.

(b)

s₁ = ut₁ + 1/2 a₁t₁²

s₁ = 0 + 1/2 (1.4)(4.9)²

s₁ = 16.8 m.

Now for the decelerated motion :

s₂ = vt₂+1/2 a₂t₂²

s₂= 6.86(1.60) + 1/2 (-1.9)(1.60)²

s₂ = 8.53 m.

So, total distance covered from the start, D :

D = s₁ + s₂

D = 16.8 + 8.53

D = 25.33 m.

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The change in the speed of the object is constant with constant increment of 5 m/s.

The change in the speed of an object is the rate at which the distance covered by the object changes with time.

The change in the speed of the object at various time is calculated as follows;

at time, t = 0 second, change in speed (Δv) = 0

at time, t = 1 second, change in speed (Δv) = 5 m/s - 0 m/s = 5 m/s

at time, t = 2 seconds, change in speed (Δv) = 15 m/s - 5 m/s = 10 m/s

at time, t = 3 seconds, change in speed (Δv) = 30 m/s - 15 m/s = 15 m/s

at time, t = 4 seconds, change in speed (Δv) = 50 m/s - 30 m/s = 20 m/s

at time, t = 5 seconds, change in speed (Δv) = 75 m/s - 50 m/s = 25 m/s

Thus, we can conclude that, the data given in the table has time which increased gradually while the speed also increase gradually but with a constant increment.

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If a man lifts a a 20-kg bucket from a well and does 6 kJ of work, the well will be 30.6 m deep.

W = m g h

W = Work

m = Mass

g = Acceleration due to gravity

h = Height

m = 20 kg

g = 9.8 m / s²

W = 6 KJ

W = 6000 J

h = W / m g

h = 6000 / 20 * 9.8

h = 30.6 m

W = m g h is derived from W = F * d. According to Newton's second law of motion, F = m a. Since the object is moving vertically upwards, a = g. Therefore, F = m g and hence W = m g h

Therefore, the well is 30.6 m deep

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D. cannon

Newton imagined a cannon on top of a mountain. Without gravity, the cannonball should move in a straight line. If gravity is present, then its path will depend on its velocity.( A and B)

If there were no forces of gravitation or air resistance, the body should follow a straight line away from Earth, in the direction that it was projected (E), If a gravitational force acts on the projectile, it will follow a different path depending on its initial velocity.

so, we can conclude the answer is

D. cannon

I hope this helps you

According to the given statement the acceleration of the car is 3ms².

Depending on whether an object is moving much faster, slower, or in a different direction, its speed may change. Examples of acceleration include a falling apple, the moon orbiting the earth and a car which has stopped at a stop sign.

Uniform acceleration, non-uniform acceleration, and average acceleration are the three different forms of accelerated motions.

Let acceleration be 'a'

v = u + at

a = v - u/t

a = 45 - 0 /15

a = 45/15

a = 3 ms²

So, acceleration will be 3 m/s² .

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B. The reactants have higher potential energy, and energy is absorbed is the statement that best describes the total energy change of the system.

The difference in the amounts of chemical energy that are stored in the products and reactants accounts for the energy change in a chemical reaction. Enthalpy refers to the system’s heat content or stored chemical energy.

Potential energy can be described as the energy which a body possess because of its position. The potential energy can also be said as stored energy. The energy diagram that shows the changes in energy is called as a chemical reaction.

Potential energy and the Reaction progress are shown in the problem and from this the reactants are seen as the substance which reacts and form one or more than one product.

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Variables typically consist of space, time, and occasionally parts of momentum. The bicycle eventually travels at 13.8 m/s.

According to Newtonian mechanics, an object's mass and velocity are combined to form its linear momentum, translational momentum, or just momentum. As a vector quantity with both a magnitude and a direction, it has both. When an object's mass (m) and velocity (v), another vector quantity, are known, the object's momentum (p) is also known.

An object's mass, velocity, and direction are related by the concept of momentum. Force is produced whenever momentum changes. As a result, the force pushing against the object is identified by a change in momentum.

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Answer:

Halite

Explanation:

The angular acceleration a of the pulley and the linear acceleration a of the bucket are 12.85 rad/s² and 4.24 m/s² respectively.

The tension in the cord  is 6.49 N.

The angular acceleration of an object is the rate of change of angular velocity with time.

Apply the principle conservation angular momentum to determine the angular acceleration of the pulley.

τ = Iα

Fr = Iα

mgr = Iα

α = mgr/I

where;

α = (1.53 x 9.8 x 0.33) / (0.385)

α = 12.85 rad/s²

The linear acceleration of the pulley is calculated as follows;

a = αr

a = 12.85 rad/s²  x  0.33 m

a = 4.24 m/s²

The tension in the cord is calculated as follows;

T = ma

T = 1.53 kg x 4.24 m/s²

T = 6.49 N

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The electrostatic force of repulsion between the two charges is equal to 0.25 x 10¹¹ N.

The coulomb's law is used to find the force between two point charges. The force can be calculated using the formula -

F = 1/4πε₀ |Q₁||Q₂|/r²

Given is two charged objects separated by a distance of 0.6 m such that one object has a charge of -5 C and the other has a charge of +2C.

The electrostatic force of repulsion between the two charges is given by-

F = 1/4πε₀ |Q₁||Q₂|/r²

F = 9 x 10⁹ x (5 x 2)/(0.6)²

F = 90 x  10⁹/0.36

F = 9 x 10¹¹/36

F = 0.25 x 10¹¹ N

Therefore, the electrostatic force of repulsion between the two charges is equal to 0.25 x 10¹¹ N.

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1.  When an object is moving away from us, the light from the object is known as redshift, and when an object is moving towards us, the light from the object is known as blueshift.

2.  A wavelength increases in size, and its frequency, and energy decrease.

3.  The frequency of a wave increases, and its wavelength decreases.

Redshift is an important term for astronomers. The term can be taken literally. The wavelengths of light are stretched and perceived as shifting toward the red portion of the spectrum. The same thing happens to sound waves when the source moves relative to the observer.

As the wave frequency decreases, the wavelength increases as long as the wave velocity remains constant. If the wave speed stays the same as the frequency decreases, it means that fewer wave peaks or troughs pass through a given point in a given time period. The number of complete wavelengths in a given unit of time is called frequency. Frequency and energy decrease with increasing wavelength.

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Metabolism is the chemical process by which your body breaks down the nutrients in foods to release energy for the cells in your body (Option 3).

The term Metabolism makes reference to all chemical reactions by which the body can obtain energy from foods by breaking them down into smaller elements. The breakdown of chemical bonds releases energy, which is used to generate Adenosine triphosphate, the energy coin of the cells.

Therefore, we can conclude that metabolism refers to the groups of pathways by which an organism breaks down nutrients such as proteins or carbohydrates in order to obtain energy for cells and perform diverse activities (e.g. growth, differentiation, etc)

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For a person who has not eaten for four days and then finally has a candy bar, your food drive will be reduced, but your food need will no.t

Food refers to any substance that is taken into the body and which contains nutrients that provide energy for the body and also provide the body with materials required for the growth and repair of body tissues.

There are seven classes of food that the body needs and they include:

Food drive refers to the urge to eat food and may be easily satiated.

Food need on the hand has to do with all the food that the body needs for healthy growth and is not easily met.

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