The smokestack of a stationary toy train consists of a vertical spring gun that shoots a steel ball a meter or so straight into the air—so straight that the ball always falls back into the smokestack. Suppose the train moves at constant speed along the straight track. Do you think the ball will still return to the smokestack if shot from the moving train? What if the train gains speed along the straight track? What if it moves at a constant speed on a circular track? Why do your answers differ?

Solution 47E Case 1 The train is moving at a constant speed along a straight track. The ball will also have the same speed due to inertia of motion. Hence it will fall back into the smokestack after being shot. Case 2 If the train gains speed after the ball is shot, the ball will fall behind the smokestack. This is because the ball will tend to maintain the initial speed of the train due to inertia of motion. Once the train gets speedier, the ball gets slower than the train’s current speed and will fall behind. Case 3 When the train is moving at a constant speed on a circular track, the ball will have a tangential motion to the circular path. The ball will tend to continue moving along the straight path. In this case, the ball will fall outside the circular track as the the train will no more move along a straight path.