Question

If a basketball player has a vertical leap of 1.56 meters, what is the total time he spends in the air? (Acceleration due to gravity: -9.81 m/s^2)

a) 0.65 seconds
b) 0.8 seconds
c) 1.0 seconds
d) 1.2 seconds

Answer 1

The basketball player spends approximately 0.565 seconds in the air.

Step-by-step explanation:

To find the total time the basketball player spends in the air, we can use the kinematic equation:

Δy = v0t + (1/2)at²

Where:

• Δy is the vertical distance, which is 1.56 meters
• v0 is the initial vertical velocity, which is 0 m/s because the player starts from the ground
• a is the acceleration due to gravity, which is -9.81 m/s²
• t is the time spent in the air

Substituting the known values into the equation, we have:

1.56 = 0 * t + (1/2) * (-9.81) * t²

Simplifying the equation, we get:

t² = (2 * 1.56) / 9.81

t² = 0.319

t ≈ √0.319

t ≈ 0.565 seconds

Therefore, the basketball player spends approximately 0.565 seconds in the air.