# Calculating the Diameter of Contact Between a Basketball and the Floor

What is the approximate diameter of contact between a basketball and the floor?

## Determining the Diameter of Contact

**Force = Pressure * Area**

The area in this case represents the contact area between the basketball and the floor, which can be estimated as a circle.

## Calculating the Pressure

Given that the basketball is inflated to a gauge pressure of 8.0 x 10^4 Pa, we first need to determine the absolute pressure by adding the atmospheric pressure to the gauge pressure:**Absolute Pressure = Gauge Pressure + Atmospheric Pressure**

Absolute Pressure = 8.0 x 10^4 Pa + 1.0 x 10^5 Pa

Absolute Pressure = 1.8 x 10^5 Pa

## Finding the Area of Contact

The area of contact between the basketball and the floor can be calculated using the formula:**Area = π * (diameter/2)^2**

Let's assume the diameter of contact between the ball and the floor is represented by D.

## Solving for the Diameter

Since the force exerted by the player is 50 N, we can rearrange the equation to solve for the diameter:**Diameter = 2 * √(Force / (Pressure * π))**

Substitute the known values into the equation and calculate the diameter:

Diameter = 2 * √(50 N / (1.8 x 10^5 Pa * π))

By calculating the diameter using the given values, we find that the approximate diameter of contact between the basketball and the floor is 4.26 cm.