Question

The vertical height attained by a basketball player who achieves a hang time of a full 1 s is about

a) 25 m.
b) 1.2 m.
c) 1 m.
d) 0.8 m.
e) more than 25 m

Answer 1

The vertical height attained by a basketball player with a hang time of 1 second is about 1.2 m. This calculation is based on the kinematic equations of motion under Earth's gravity.

Step-by-step explanation:

To answer the student's question concerning the vertical height attained by a basketball player with a hang time of 1 second, we can use the kinematic equations of motion. The formula h = 1/2 g t2 describes the height h (in meters) achieved after a time t (in seconds), where g is the acceleration due to gravity (9.8 m/s2 on Earth). Plugging in the values, we get h = 1/2 * 9.8 m/s2 * (1 s / 2)2 = 1.225 m. The correct answer is therefore around 1.2 m, making option (b) the closest correct choice.

In regards to the additional information provided:

1. For a basketball player to rise 0.750 m, the required initial vertical velocity can be found using the kinematic formula vf2 = vi2 + 2gh, where vf is the final velocity (0 m/s at the highest point), vi is the initial velocity we need to find, g is gravity, and h is the height. Solving for vi gives us the required initial vertical velocity.
2. To calculate how far from the basket the player must start his jump to reach his maximum height at the same time as he reaches the basket, we use horizontal motion equations since the horizontal velocity is constant.