Find the time of the particle?

Question

A basketball player, standing near the basket to grab a rebound, jumps 65.3 cm vertically. How much time does the player spend in the top 14.9 cm of his jump?

How much time does the player spend in the bottom 14.9 cm of the jump?

Answer 1

If t is the time to fall 14.9 cm starting from rest:

14.9 = 981 t^2 / 2

t = sqrt(2 * 14.9 / 981) sec.

The time in the top 14.9 cm. is:

2t = 2 sqrt(2 * 14.9 / 981)

= 0.349 sec.

If t1 is the time to fall 65.3 cm starting from rest,

and t2 is the time to fall 65.3 - 14.9 = 50.4 cm:

65.3 = 981 t1^2 / 2

t1 = sqrt(2 * 65.3 / 981)

= 0.3649 sec.

t2 = sqrt(2 * 50.4 / 981)

= 0.3205 sec.

The time spent in the bottom 14.9 cm. is:

2(t1 - t2)

= 2(0.3649 - 0.3205)

= 8.86 * 10^(- 2) sec.