At the highest point in its parabolic trajectory, a shell explodes into two fragments. Is it possible for both fragments to fall straight down after the explosion? Why or why not?

A ball is thrown into the air and follows a parabolic trajectory. At the highest point in the trajectory, (a) the velocity is zero, but the acceleration is not zero. (b) both the velocity and the acceleration are zero. (c) me acceleration is zero, but the velocity is not zero. (d) neither the acceleration nor the velocity are zero.

When an object breaks into two pieces (explosion, radioactive decay, recoil, etc.), the lighter fragment gets more kinetic energy than the heavier one. This is a consequence of momentum conservation, but can you also explain it using Newton’s laws of motion?

At the highest point in its parabolic trajectory, a shell explodes into two fragments. Is it possible for both fragments to fall straight down after the explosion? Why or why not?

A machine gun is fired at a steel plate. Is the average force on the plate from the bullet impact greater if the bullets bounce off or if they are squashed and stick to the plate? Explain.

In a zero-gravity environment, can a rocket-propelled spaceship ever attain a speed greater than the relative speed with which the burnt fuel is exhausted?

A tennis player hits a tennis ball with a racket. Consider the system made up of the ball and the racket. Is the total momentum of the system the same just before and just after the hit? Is the total momentum just after the hit the same as 2 s later, when the ball is in midair at the high point of its trajectory? Explain any differences between the two cases.

If the momentum of a pair of point objects is equal to zero, must the kinetic energy of those objects also be zero?

(a) When a large car collides with a small car, which one undergoes the greater change in momentum: the large one or the small one? Or is it the same for both? (b) In light of your answer to part (a), why are the occupants of the small car more likely to be hurt than those of the large car, assuming that both cars are equally sturdy?

When rain falls from the sky, what becomes of the momentum of the raindrops as they hit the ground? Is momentum conserved for a system consisting of just a raindrop? Is momentum conserved if the system includes a raindrop and the earth? Explain.

Since for a particle the kinetic energy is given by $K=\frac{1}{2} m v^{2}$ and the momentum by $\vec{p}=m \vec{\boldsymbol{v}}$, it is easy to show that $K=p^{2} / 2 m$. How, then, is it possible to have an event during which the total momentum of the system is constant but the total kinetic energy changes?

A net force with $x$-component $\sum F_x$ acts on an object from time $t_1$ to time $t_2$. The $x$-component of the momentum of the object is the same at $t_1$ as it is at $t_2$, but $\sum F_x$ is not zero at all times between $t_1$ and $t_2$. What can you say about the graph of $\sum F_x$ versus $t$ ?

The kinetic energy of the Ping-Pong ball is larger after its interaction with the bowling ball than before. From where does the extra energy come? Describe the event in terms of conservation of energy.

When rain falls from the sky, what happens to its momentum as it hits the ground? Is your answer also valid for Newton’s famous apple?