Question

A ball is projected horizontally from the top of a building. One second later, another ball is projected horizontally from a point with the same initial velocity. At what point will the balls be closest to each other?

a. At the beginning of their motion
b. At the midpoint of their trajectory
c. At the end of their motion
d. It cannot be determined from the information given

Answer 1

The two balls projected horizontally from a building will be closest to each other at the beginning of their motion due to the consistent effect of gravity on both balls regardless of their horizontal velocities.

Step-by-step explanation:

The student asked at what point two balls projected horizontally from the top of a building, one second apart with the same initial velocity, would be closest to each other. To find the closest point of two objects in projectile motion, we need to understand that horizontal motion and vertical motion are independent of each other. Since both balls have the same horizontal velocity and horizontal motion does not affect the vertical motion, the only difference between the two balls' motion is the vertical displacement due to gravity.

As both balls fall, gravity accelerates them at the same rate, regardless of their horizontal velocities. Since the second ball starts its fall one second after the first ball, it will always be higher than the first ball until it hits the ground. Therefore, the two balls will be closest to each other right at the beginning of their motion, before the effects of gravity have had a chance to create a larger vertical separation between the two. Hence, the correct option is a. At the beginning of their motion.