A basketball referee tosses the ball straight up for the starting tipoff. At what velocity must a basketball player leave the ground to rise 1.25 m above the floor in an attempt to get the ball?

To determine the velocity at which the basketball player must leave the ground to rise 1.25 meters above the floor, we can use the following kinematic equation:

\[
v^2 = u^2 + 2as
\]

Where:
- \( v \) is the final velocity at the highest point (which is 0 m/s because the player momentarily stops rising at the peak of the jump),
- \( u \) is the initial velocity (the velocity we want to find),
- \( a \) is the acceleration (which is \(-9.81 \, \text{m/s}^2\), the acceleration due to gravity), and
- \( s \) is the displacement (1.25 meters in this case).

Since \( v = 0 \) at the maximum height, the equation simplifies to:

\[
0 = u^2 + 2(-9.81)(1.25)
\]

Solving for \( u \):

\[
u^2 = 2 \times 9.81 \times 1.25
\]

\[
u^2 = 24.525
\]

\[
u = \sqrt{24.525} \approx 4.95 \, \text{m/s}
\]

Therefore, the basketball player must leave the ground with an initial velocity of approximately **4.95 m/s** to rise 1.25 meters above the floor.

Would you like to know more details, or do you have any questions?

Here are five related questions for further exploration:
1. How long will it take for the player to reach the maximum height of 1.25 meters?
2. What is the total time the player will be in the air during the jump?
3. If the player weighed 80 kg, what would be the kinetic energy at the point of takeoff?
4. How does the jump height change if the player leaves the ground at 5.5 m/s?
5. What factors could affect a player's actual jump height in a real-world scenario?

**Tip:** When solving physics problems involving motion, it's often helpful to list all known quantities and identify which kinematic equations relate them to the unknown quantity you're solving for.

Learn how to calculate the initial velocity required for a basketball player to rise 1.25 meters above the floor using kinematic equations. This problem covers key concepts in kinematics and projectile motion, with an emphasis on solving for initial velocity and understanding gravitational acceleration. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation