A ball is dropped from a height of $20m$. If the coefficient of restitution is $0.9$, what will be the height attained after the first bounce?

The correct option is B

$16.2m$

Step 1: Definition of coefficient of restitution.

1. It is defined as the ratio of the final to initial velocity between two objects after their collision.
2. It is generally denoted by ‘$e$’ and its range lies between $0$ to $1$.

Given data: Let height of the ball before collision, $h=20m$

Coefficient of restitution, $e=0.9$

Step 2: Calculating the height of a ball after the first bounce.

Hence, height of a ball after collision, $h^{\text{'}}$is given by:

$$\begin{gathered} h^{\text{'}}={\left(e\right)}^2\times h \\ \Rightarrow h^{\text{'}}={(0.9)}^2\times 20 \\ \Rightarrow h^{\text{'}}=16.2m \end{gathered}$$

Hence, option(B) is the correct answer.