Question

A ball hits a wall horizontally at $6.0m{{s}^{-1}}$. It rebounds horizontally at $4.4m{{s}^{-1}}$. The ball hit the wall for 0.040 s. What is the acceleration of the ball?

Answer 1

We will make use of the law of motion formula to find the value of the acceleration. The velocity with which a ball is hit should be considered as the initial velocity and the velocity with which the ball rebounds should be considered as the final velocity and even the value of the time is given. Using all these values we will find the acceleration of the ball.
Formula used:
$v=u+at$

Complete answer:
From the data, we have the data as follows.
A ball hits a wall horizontally at$6.0m{{s}^{-1}}$. This implies that the initial velocity of the ball is$6.0m{{s}^{-1}}$.
The ball rebounds horizontally at$4.4m{{s}^{-1}}$. This implies that the final velocity of the ball is $-4.4m{{s}^{-1}}$.
The negative sign indicates the opposite direction.
The time taken by the ball is 0.040 s.
The law of motion formula is given as follow
$v=u+at$
Where v is the final velocity, u is the initial velocity, a is the acceleration and t is the time taken.
Now substitute the given values in the above equation. So, we get,

& -4.4=6+a(0.040) \\\ & \Rightarrow -10.4=0.04a \\\ \end{aligned}$$ Continue the further calculation to find the value of the acceleration $$\begin{aligned} & a=-\dfrac{10.4}{0.04} \\\ & \Rightarrow a=-260m{{s}^{-2}} \\\ \end{aligned}$$ Therefore, the acceleration of the ball hit horizontally to the wall that got rebounded is $$-260m{{s}^{-2}}$$. The negative sign indicates the opposite direction. **Note:** The units of the parameters should be taken care of. Even the signs of the parameters should be taken care of. As, in this case, the velocity with which the ball rebounds should be considered to be negative. These are the main points to be noted down while solving these types of problems.