Question

A boy releases a $0.5kg$ ball on the frictionless floor with the speed of $20m/s$. The ball gets deflected by an obstacle on the way. After deflection it moves with $5\%$ of its initial kinetic energy. What is the speed of the ball now ?

• A. $14.41m/s$
• B. $1m/s$
• C. $19m/s$
• D. $4.47m/s$

Answer 1

The correct option is D

$4.47m/s$

Step 1 Given data:

Mass of the ball, $m=0.5kg$

Initial Speed of the ball, $v_i=20m/s$

The final kinetic energy of the ball, $K{E}_f=5\%\left(K{E}_i\right)$ where, $K{E}_i$ is the initial kinetic energy

Step 2: Calculate the initial and final kinetic energies of the system

$K{E}_i=\frac{1}{2}m{v_i}^2=\frac{1}{2}*m*{\left(20\right)}^2$…..(i)

Let the final speed be $v$

$K{E}_f=\frac{1}{2}m{v}^2$…………(ii)

Step 3 Find the speed of the ball after a deflection

As we know, the final kinetic energy is $5\%$ of the initial kinetic energy,

$$\begin{gathered} K{E}_f=\frac{1}{2}m{v}^2=5\%K{E}_i \\ \Rightarrow \frac{1}{2}*0.5*v^2=\frac{5}{100}*\frac{1}{2}*0.5*{20}^2 \\ \Rightarrow v^2=\frac{2000}{100}=20 \\ \Rightarrow v=\sqrt{20}=2\sqrt{5}m/s=4.47m/s \end{gathered}$$

Hence the speed of the ball is $4.47m/s$ . Hence Option D is correct.