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A child in a slowly moving car tosses a ball upward. It rises to a point below the roof of the car and falls back down, at which point the child catches it. During this time the car neither speeds up nor slows down, and does not change direction.

What force(s) act on the ball between the instant of its release and the instant at which it is caught? You can ignore air resistance.

The gravitational force exerted by the Earth on the ball, i.e., the weight of the ball, will act at all times.

During the interval between release and catch, the child's hand is not in contact with the ball and cannot exert a force on it.
 

During the interval between release and catch, the automobile is not in contact with the ball and cannot exert any force on it by means of contact.
 

Other than negligible air resistance, and the even more negligible gravitational interaction between the car and the ball, the only force acting on the ball is its weight.

STUDENT RESPONSE:

The force of gravity is acting on the object downwards. The force of the toss is acting upwards on the ball. The initial velocity of the ball is moving it forwards. </p>

VERY IMPORTANT CLARIFICATION/CORRECTION BY INSTRUCTOR: 

The specified interval is between release and catch.

For the given interval no force is exerted on the ball by the child or the car.  Neither is in any sort of contact with the ball, and neither child nor car can exert a force (excepting the very small gravitational force they exert) on something it isn't in contact with.  

The Earth is massive enough to exert a significant gravitational force on the ball.

Nothing is moving the ball forward. It doesn't take anything to move the ball forward. This is the essence of Newton's First Law, which tells us that the ball will move in a straight line at constant velocity unless a force causes it to change speed and/or direction. During the specified interval, the toss is over and only gravity is acting on the ball.

STUDENT QUESTION

Does the child throwing the ball into the air not count as a force?

INSTRUCTOR RESPONSE

The question asked about the motion from the instant of release to the instant at which it is caught. You could assume that a force from the child's hand is present at each of these instants, but only for each instant (one at the beginning and one at the end of the specified interval), so neither force has any time in which to change the momentum. The motion during the interval is therefore the same whether or not you assume that those forces are present.
 

What happens to the speed of the ball between release and catch? Describe in some detail; a graph of speed vs. clock time would also be appropriate.

The ball slows as it rises, then speeds up as it falls.  The acceleration, which is the rate of change of velocity with respect to clock time and is hence the slope of the v vs. t graph, is constant with a slope equal to the acceleration of gravity.  The v = 0 point corresponds to the instant the ball comes to rest.  The velocity is negative on one side of this point, positive on the other.

The speed is the magnitude of the velocity, so the speed vs. clock time graph decreases up to the v = 0 point, then increases to the right of this point.  The steepness is the same on both sides, but the slope to the left of the v = 0 point is negative, while the slope to the right is positive.

Put another way:  As the ball rises to its apex its speed will decrease at a constant rate with respect to clock time. As it then falls its speed increases with respect to clock time, again at a constant rate. The speed vs. clock time graph therefore consists of two straight-line segments, forming a V.

Describe the path of the ball as it would be observed by someone standing along the side of the road.

As observed from the side of the road the ball travels forward at constant speed as it rises then falls.

The ball speeds up in the vertical direction but not in the horizontal.

The path is therefore curved--in fact it can be shown that the path is parabolic.
 

The ball is observed from the roadside to speed up in the vertical direction but not in the horizontal, causing the path to curve (as it turns out the path is in fact parabolic).

COMMON STUDENT RESPONSE

since the vehicle was moving, the force is also transferred to the ball and the ball does not have a straight path.

INSTRUCTOR CORRECTION

There is no force on the ball associated with the constant-velocity motion of the vehicle.

How would the path differ if the child was coasting along on a bicycle? What if the kid didn't bother to catch the ball?

If the speed is not too great air resistance won't have much effect and the path of the ball will be the same, both as seen by the child and as seen by someone standing along the road.

If the speed is greater the air resistance will cause the ball to accelerate backwards relative to the child.

To a person standing by the road, the path will appear much like the parabolic path described previously, but the position of the ball will fall progressively further and further behind the parabola, so that the arc will not be as symmetric as the ideal parabolic arc.

PARTIAL STUDENT RESPONSE

the force from the bike is still working on the ball as it falls.

INSTRUCTOR RESPONSE

The bike exerts no force as the ball falls. There is no significant force on the ball in the forward direction so its horizontal acceleration is zero (ignoring air resistance). Not only does it not take a force for the ball to continue moving forward at constant velocity, if there was a net force on the ball in the forward direction, it would not move with constant velocity in that direction.

What if the child holds the ball out of an open window and drops it. If the ball is dense (e.g., a steel ball) and the car isn't moving very fast, air resistance will have little effect. Describe the motion of the ball as seen by the child. Describe the motion of the ball as seen by an observer by the side of the road.

If air resistance is insufficient to significantly slow the ball, it will continue its horizontal motion alongside the car.  The child will therefore see the ball drop straight down, just as it would in the car.

The observer will see a half of a parabolic path, starting at the high point (the vertex of the parabola) and curving downward until it reaches the level of the road. 

STUDENT ANSWER   The ball will fall straight down from the child’s hand when it is released as seen when an outside observer watches it. When the child watches it, the ball will fall straight down also.

INSTRUCTOR RESPONSE

The observer will see the ball drop, but will also see the ball move forward at the speed of the car. If the car and the child were suddenly rendered invisible, the observer would see it move in the same familiar manner as a ball projected forward at a velocity matching that of the car.