Question

Compare the time in the air of a basketball player who jumps 1.0 m vertically off the floor with that of a player who jumps 0.3 m vertically.

a) The player jumping 1.0 m is in the air for a longer time.
b) The player jumping 0.3 m is in the air for a longer time.
c) Both players are in the air for the same time.
d) The time in the air cannot be determined without more information.

Answer 1

The player who jumps 0.3 m vertically will spend more time in the air compared to the player who jumps 1.0 m.

Step-by-step explanation:

When comparing the time in the air of a basketball player who jumps 1.0 m vertically off the floor with that of a player who jumps 0.3 m vertically, the player who jumps 0.3 m will be in the air for a longer time.

We can use the kinematic equation for vertical motion to calculate the time:

∆y = v0yt + 0.5at2

Since both players start from rest (v0y = 0), the equation simplifies to:

∆y = 0.5at2

Since the only difference between the two players is the height they jump, the time in the air is directly proportional to the square root of the height jumped. Therefore, the player who jumps 0.3 m will spend more time in the air compared to the player who jumps 1.0 m.