Question

A basketball player, about to "dunk" the ball, jumps 76 cm vertically. bout to "dunk" the ball, jumps 76 cm vertically.

(a) How much (total) time does the player spend in the top 25 cm of this jump?

(b) How much (total) time does the player spend in the bottom 25 cm of this jump? ms (c) Does this help explain why such players seem to hang in the air at the tops of their jumps?

Answer 1

Use the formuls and

velocity at the top of jump is zero.

acceleration is acceleration due to gravity (upward vectors are positive)

Hence time taken to jump 0.76 m is

Initial velocity is

(a)

Similarly time taken to reach a height is given by

Solving the above quadratic equation,

Hence the player is spending in the top 25 cm of the jump while going up and an equal time while coming down.

Hence total time spent in the top 25 cm is

(b)

Similarly time taken to reach a height is given by

Solving the above quadratic equation,

Hence the player is spending in the bottom 25 cm of the jump while going up and an equal time while coming down.

Hence total time spent in the bottom 25 cm is

(c)

Hence time spent in the bottom 25 cm is nearly one third of time spent in the top 25 cm. hence the player seems to hang in the air at the top of jump.