A basketball has a coefficient of restitution of 0.821 in collisions with the wood floor of a basketball court. The ball is dropped on such a floor from a height of 2.07 m . How high is its fourth bounce?

The height of its fourth bounce = 0.43m

Explanation:

The coefficient of restitution denoted by (e), is the ratio that shows the  final velocity to initial relative velocity between two objects after collision

IT is given by the formula in terms of height as

Coefficient of Restitution, e  = √(2gh))/√(2gH) = √(h/H)

Where

Coefficient of Restitution, e= 0.821

H = 2.07 m

At fourth bounce ,   we have that

Coefficient of Restitution, e⁴  =√(h₄/H)  

Putting the given values and solving , we have,

e⁴  =√(h₄/H)  

= 0.821⁴ = √(h₄/2.07)

 (0.821⁴ )² =h₄/2.07

0.2064 x 2.07 = 0.427 = 0.43

At  fourth bounce,  h₄ height = 0.43m