Question

In a square cut, the speed of the cricket ball changes from 30 \[m{{s}^{-1}}\] to 40 \[m{{s}^{-1}}\] during the time of its contact \[\Delta t=0.01s\] with the bat. If the ball is deflected by the bat through an angle of \[\theta ={{90}^{0}}\], find the magnitude of the average acceleration of the ball (in \[\times {{10}^{2}}m{{s}^{-2}}\]) during the square cut.

Answer 1

Hint: We need to understand the impact caused by the batsman on the ball during the square-cut strike on the ball. The change in velocity of the ball is due to the impulse on the ball as the man hits it with the bat with his muscle power resulting in an acceleration.

Complete step-by-step solution
We know that in the game of cricket, a bowler throws a ball at the batsman with a speed. The ball reaching the batsman with a velocity is hit by the batsman with his bat. The hitting is often associated with a deviation of the ball towards another side with an increase in the velocity of the ball.
In our situation, the batsman strikes the ball coming with an initial velocity of 30\[m{{s}^{-1}}\], deviates into a angle of \[\theta ={{90}^{0}}\] and the velocity of the ball is increased to 40 \[m{{s}^{-1}}\].
We know that the average acceleration of a body is defined as the ratio of change in velocity to the time taken for this change. Here, the bat has a contact time of \[\Delta t=0.01s\] with the ball. So, we can easily find the average acceleration of the ball as –
\[\begin{align}
  & a=\dfrac{\text{final velocity - initial velocity}}{\text{time taken}} \\
 & \Rightarrow a=\dfrac{\Delta v}{\Delta t} \\
 & \Rightarrow a=\dfrac{40m{{s}^{-1}}-30m{{s}^{-1}}}{0.01} \\
 & \therefore a=10\times {{10}^{2}}m{{s}^{-2}} \\
\end{align}\]
The acceleration of the ball due to the impact caused by the bat is \[a=10\times {{10}^{2}}m{{s}^{-2}}\].
This is the required solution.

Note: In the game of cricket, the bowler uses different tactics to trick the batsmen. He can swing, spin, or perform different possible methods for throwing the ball which can baffle the batsmen. The direction of the ball after striking the bat is dependent on the throws.