Suppose you are driving in a convertible with the top down. The car is moving to the right at a constant velocity. As Figure 3.11 illustrates, you point a rifle straight upward and fire it. In the absence of air resistance, where would the bullet land—behind you, ahead of you, or in the barrel of the rifle?

Figure 3.11  The car is moving with a constant velocity to the right, and the rifle is pointed straight up. In the absence of air resistance, a bullet fired from the rifle has no acceleration in the horizontal direction. As a result, the bullet would land back in the barrel of the rifle.

Reasoning and Solution If air resistance were present, it would slow down the bullet and cause it to land behind you, toward the rear of the car. However, air resistance is absent, so we must consider the bullet’s motion more carefully. Before the rifle is fired, the bullet, rifle, and car are moving together, so the bullet and rifle have the same horizontal velocity as the car. When the rifle is fired, the bullet is given an additional velocity component in the vertical direction; the bullet retains the velocity of the car as its initial horizontal velocity component, since the rifle is pointed straight up. Because there is no air resistance to slow it down, the bullet experiences no horizontal acceleration. Thus, the bullet’s horizontal velocity component does not change. It retains its initial value, and remains matched to that of the rifle and the car. As a result, the bullet remains directly above the rifle at all times and would fall directly back into the barrel of the rifle, as the drawing indicates. This situation is analogous to that in Figure 3.9, where the care package, as it falls, remains directly below the plane.

Related Homework: Conceptual Question 12, Problem 34