A, under what conditions does the resultant vector have a magnitude equal to A + B?

Explanation: 90/2 = 45

(a) The vector lies at a 60 degree angle with two axes along which the component lie.

(b) The vector lies at a 45 degree angle with two axes along which the component lie.

(c) The vector lies at a 30 degree angle with two axes along which the component lie.

would have to drop to zero. However, velocity of x

always remains equal to its initial value; therefore,

the velocity and the acceleration can never be parallel.

(a) At what point in the motion will the balls be closest to each other?

They stay equidistant from each other throughout the motion.

the instant the first ball hits the ground

the instant the second ball is projected

one second after the second ball is projected

(b) Will the first ball always be traveling faster than the second?

Yes

No

(c) What will be the time difference between them when the balls hit the ground?

one second

It depends on the height of the building.

no time difference

between one and ten seconds

(d) Can the horizontal projection velocity of the second ball be changed so that the balls arrive at the ground at the same time?

Yes

No

(d) A rocket moves through the sky after its engines have failed.

Explanation:There is only one force acting on an object in ideal projectile motion problems- gravity.

(a) A ball is thrown in an arbitrary direction.

(b) A jet airplane crosses the sky with its engines thrusting the plane forward.

(c) A rocket leaves the launch pad.

(d) A rocket moves through the sky after its engines have failed.

(e) A stone is thrown under water.

(b) The passenger on the train would see the ball fall behind the position it would reach in the absence of the acceleration. The stationary observer outside the train would see the ball follow the same path as before (assuming the initial release velocity is the same).

(c) If the train were accelerating, the ball would fall behind the position it would reach in the absence of the acceleration.

(a) Describe the path of the ball as seen by the passenger.

(b) Describe the path as seen by a stationary observer outside the train.

(c) How would these observations change if the train were accelerating along the track?

(a) Is the projectile a freely falling body?

(b) What is its acceleration in the vertical direction? (Let up be the positive direction.)

(c) What is its acceleration in the horizontal direction?

Its velocity is not zero, but its acceleration is zero.

Its velocity and its acceleration are both zero.

Its velocity is perpendicular to its acceleration.

Its acceleration depends on the angle at which the ball was thrown.

None of the above statements are true.

***Remember that acceleration due to gravity is independent of mass.

The blue ball reaches the ground first.

The balls reach the ground at the same instant.

The red ball reaches the ground first.

Both balls hit the ground with the same speed.

None of the above statements are true.

It has an acceleration with a direction that cannot be determined from the information given.

It has an acceleration component in the direction of its velocity.

It has an acceleration directed toward the center of its path.

It has zero acceleration.

It has an acceleration directed away from the center of its path.

(i) Of the curves shown in the figure above, which best describes the path followed by the apple as seen by a stationary observer on the ground, who observes the truck moving from his left to his right?

(a) curved left

(b) 180° vertical

(c) curved right

(d) slanted at a 45° left

(e) slanted at a 45° right

(ii) Of the curves shown in the figure above, which best describes the path as seen by an observer sitting in the truck?

In the y axis: (+)

(In 4 quadrants, Vector A is headed along the (+) y axis and (-) axis. Vector B is travelling towards the (-) y axis along the (+) axis. )

(a) Vector A

In the y axis: (-)

(In 4 quadrants, Vector A is headed along the (+) y axis and (-) axis. Vector B is travelling towards the (-) y axis along the (+) axis. )

(b) Vector B

In the y axis: (-)

Explanation: (the resultant vector is in quadrant IV)

(In 4 quadrants, Vector A is headed along the (+) y axis and (-) axis. Vector B is travelling towards the (-) y axis along the (+) axis. )

(c) Vector A + Vector B

(c) gas pedal

(d) brake

Explanation:

Turning the steering wheel would cause angular momentum and angular acceleration of the wheel itself, also when you turn the car in any direction you are causing a new acceleration in that direction, where it was previously zero.

A gas pedal causes (+) acceleration

A brake causes (-) acceleration

(a) none of these

(b) steering wheel

(c) gas pedal

(d) brake

Explanation:B is only correct assuming that he is running in straight line.

a) is wrong because the ball will have an additional horizontal component of velocity and will be always ahead of the runner who is traveling at the same speed(velocity)

c) is wrong because horizontal component of ball will be larger than that o f the runner

(a) Throw the ball at an angle of about 45° with the horizontal and maintain the same speed.

(b) Throw the ball straight up in the air and maintain the same speed.

(c) Throw the ball straight up in the air and slow down to catch it.

Explanation:

at the peak, velocity is horizontal so vertical component becomes zero and acceleration is always vertically downwards

1. everywhere along the projectile’s path

2. at the peak of its path

3.nowhere along its path

4. not enough information given at the peak of its path

Explanation: w = mg and g decreases with altitude. Thus to get a good buy, purchase it in Denver. If it were sold by mass, it would not matter where you bought it.

Explanation: If it were sold by mass, it would not matter where you bought it.

(a) Identify all the external forces acting on the ball and the reaction to each.

(b) If the ball is dropped, what force is exerted on it while it is falling? Identify the reaction force in this case. (Neglect air resistance.)

(a) As she pumps a barbell up and down, what happens to the reading on the scale?

At the top of the motion and as the barbell is allowed to move back downward, the scale reading is less than the combined weights.

(b) Suppose she is strong enough to actually throw the barbell upward. How does the reading on the scale vary now?

(No Response)

(a) a man takes a step

(b) a snowball hits a girl in the back

(c) a baseball player catches a ball

(d) a gust of wind strikes a window

(a) a projectile in motion in the presence of air resistance

(b) a rocket leaving the launch pad with its engines operating

Horizontally, we have friction (in direction of motion) and drag (against direction of motion); how these compare determine whether or not the runner is accelerating. If there is no acceleration and no drag, then friction is not required to propel him forward.

(c) an athlete running along a horizontal track

Explanation: Whenever the rope is stationary, or when it moves with a constant speed, and when we neglect the mass of the rope, the pull on both sides will be the same.

This is equal to the tension of the rope.

Explanation: It’s the same; if the force against the ground (usually called the force of Friction or Fs) was not there they would not be able to put the tension upon the rope.

Explanation: Gravity always acts with 9.8m/s^2 of acceleration unless there is an external force acting, and there is no external force, so the acceleration remains constant. Because there is no force to slow it down, the velocity (or speed) increases.

(a) Its speed increases and its acceleration decreases.

(b) Its speed and acceleration remain constant.

(c) Its speed increases and its acceleration remains constant.

(d) Both its speed and acceleration increase.

(e) Both its speed and acceleration decrease.

Explanation: The friction force = (coefficient of friction) * (weight of crate) * (cosine of angle)

The friction force is always in the opposite direction of motion.

So, the friction force is preventing the crate from sliding down the ramp.

The gravitational force acting down the ramp = (weight of crate) * (sine of angle)

The gravitational force acting down the ramp is causing the crate to slide down the ramp.

If the crate remains stationary, the friction force must greater than or equal to the gravitational force acting down the ramp.

(a)It is greater than the component of the gravitational force acting down the ramp.

(b) It is at least equal to the weight of the crate.

(c)It is equal to the component of the gravitational force acting down the ramp.

(d) It is larger than the weight of the crate.

(e)It is equal to μsn.

Explanation: Newton’s 1st law

Explanation: This might be true for some cases, but not all cases. For example, an object can be moving and so long as there is no opposing unbalanced force acting on it, it will continue to move and be at equilibrium.

(a)The velocity is constant.

(b) The acceleration of the object is zero.

(c) The object must be at rest.

(d) The speed of the object remains constant.

(e) The net force acting on the object is zero.

Explanation: According to newtons 2nd law of motion, we know that

F = ma and can determine that a = f/m

Here, the force remains constant but the mass decreases, and we know that mass is inversely proportional to acceleration. So, we can determine that acceleration increases.

(a) It remains constant.

(b) It increases and then decreases.

(c) It increases at a steady rate.

(d) It decreases at a steady rate.

(e) It decreases and then increases.

Explanation: the friction force is responsible for both the forward motion of the truck as m*a in the opposite direction and the acceleration forward of the crate.

(a)the normal force

(b) the force of gravity

(c) the force of friction between the crate and the floor of the truck

(d) the “ma” force

(e) none of these

Explanation: mass doesn’t change due to gravity

(a) An astronaut’s weight is the same on the Moon as on Earth.

(b) An astronaut’s mass is the same on the International Space Station as it is on Earth.

(c) Earth’s gravity has no effect on astronauts inside the International Space Station.

(d) An astronaut’s mass is greater on Earth than on the Moon.

(e) None of these statements are true.

(a) An object can move even when no force acts on it.

(b) If an object isn’t moving, no external forces act on it.

(c) If a single force acts on an object, the object accelerates.

(d) If an object accelerates, a force is acting on it.

(e) If an object isn’t accelerating, no external force is acting on it.

(f) If the net force acting on an object is in the positive x-direction, the object moves only in the positive x-direction.

Because the value of g is smaller on the Moon than on the Earth, someone possessing 1 newton of gold on the

Moon has more gold than does a person having 1 newton of gold on Earth.

Explanation: In case (i), the scale records the tension in the rope attached to its right end. The section of rope in the man’s hands has zero acceleration, and hence, zero net force acting on it. This means that the tension in the

rope pulling to the left on this section must equal the force F the man exerts toward the right on it. The scale

reading in this case will then be F.

In case (ii), the person on the left can be modeled as simply holding the rope tightly while the person on the right pulls. Thus, the person on the left is doing the same thing that the wall does in case (i). The resulting scale reading is the same whether there is a wall or a person holding the left side of the scale.

Explanation: The tension in the rope has a vertical component that supports part of the total weight of the woman and

sled. Thus, the upward normal force exerted by the ground is less than the total weight.

(a) possibly greater or less than the total weight, depending on the size of the weight relative to the tension in the rope

(b) greater than the total weight

(c) less than the total weight

(d) equal to the total weight

Explanation: The tension in the rope has a vertical component that supports part of the total weight of the woman and

sled. Thus, the upward normal force exerted by the ground is less than the total weight.

(a) into the wall

(b) out from the wall

(c) upward

(d) downward

Explanation: The static friction force between the bottom surface of the crate and the surface of the truck bed is the net horizontal force on the crate that causes it to accelerate. It is in the same direction as the acceleration, toward the east.

(a) to the west

(b) to the east

(c) there is no friction force, because the crate isn’t sliding

Explanation: it is easier to attach the rope and pull. In this case, there is a component of your applied force that is upward. This reduces the normal force between the sled and the snow. In turn, this reduces the friction force between the sled and the snow, making it easier to move. If you push from behind, with a force with a downward component, the normal force is larger, the friction force is larger, and the sled is harder to move.

(a) attaching a rope to the front of the sled and pulling with a force at 30° above the horizontal (Fig. b)

(b) pushing her from behind by applying a force downward on her shoulders at 30° below the horizontal (Fig. a)

Neglecting air friction effects, what path does the package travel as observed by the pilot?

If the ball is thrown at half the given speed, then it will land:

If the speed of the boat relative to the water is increased, what happens to the angle?

Explanation: Consider how the components of force vector F 1 and vector F 2 must be related to produce an acceleration with a component in the desired direction. Consider whether the condition can be satisfied for a force vector F 2 that has no component pointing directly across the river. Write the expression for the contributions to the net force component in a direction perpendicular to the river and consider how F1, F2 , and the two angles must be related to produce a force component in the desired direction.

(d) the tension T1

Which of these would increase if a second traffic light were attached to the first? Assume the cables do not change their lengths. (Select all that apply.)

(a) the tension T2

(b) the angle of the cable with tension T2

(c) the angle of the cable with tension T1

(d) the tension T1

2. (b) The magnitude of the normal force would be smaller.

1. Consider the same scenario on a hill with a steeper slope.

Would the magnitude of the tension in the rope get larger, smaller, or remain the same as before?

(a) The magnitude of the tension force would be greater.

(b) The magnitude of the tension force would be smaller.

(c) The magnitude of the tension force would remain the same.

2. How would the normal force be affected?

(a) The magnitude of the normal force would be greater.

(b) The magnitude of the normal force would be smaller.

(c) The magnitude of the normal force would remain the same

(d) larger maximum angle.

(a) larger component of gravitational force along the ramp at the maximum angle.

(b) larger component of normal force at the maximum angle.

(c) smaller maximum angle.

(d) larger maximum angle.

(e) smaller component of gravitational force along the ramp at the maximum angle.

the downward force of gravity on the boat

What other forces act on the airboat? (Select all that apply.)