Question

Review Conceptual Example 15 before attempting this problem. Two identical pellet guns are fired simultaneously from the edge of a cliff. These guns impart an initial speed of 22.3 m/s to each pellet. Gun A is fired straight upward, with the pellet going up and then falling back down, eventually hitting the ground beneath the cliff. Gun B is fired straight downward. In the absence of air resistance, how long after pellet B hits the ground does pellet A hit the ground?

Answer 1

As pellet A rises from the top of the cliff to its maximum height, its velocity will decrease from 22.3 m/s to 0 m/s at the rate of 9.8 m/s² each second. As pellet A falls from its maximum height to the top of the cliff, its velocity will decrease from 0 m/s to 22.3 m/s at the rate of 9.8 m/s² each second. At the end of this time, pellet A will have the same downward velocity at pellet B initially has. The difference of time is equal to the sum of these two times.

v_f = v_i – a * t
0 = 22.3 – 9.8 * t
t = 22.3 ÷ 9.8 = 2.2755 sec
This is approximately 2.2755 seconds.
Total time = 44.6 ÷ 9.8 = 4.5510 sec
This is approximately 4.5510 seconds.