question_answer

In a football match between England and Brazil, the Brazilian star Ronaldo strikes the ball towards the goal but an England defender exactly in front of him, kicks it back. The ball struck the defender's foot at the speed at     10 m/s and it rebounces back after kicking at 20m/s. The time of impact was 0.2 sec and mass of the ball is 1/2 kg. Find the average force exerted by the defender on the ball.

Answer:

\[u=10m/s\] \[v=-20m/s\] \[t=0.2\sec \] \[m=1/2kg\] When the defender strikes the ball, he is exerting the impulsive force on the foot ball. We know that, Impulse\[(1)=F\times t\] \[\Rightarrow \,\,mv-mu=F\times t\,\,\Rightarrow \]average force\[=F=\] \[\frac{mv-mu}{t}=m\left( \frac{v-u}{t} \right)\] ??(1) \[\therefore \]substituting the above values in (1), we have \[F=\frac{\frac{1}{2}(-20-10)}{0.2}=\frac{\frac{1}{2}(-30)}{0.2}=\frac{-15}{0.2}=-75\,\,N\] Therefore, average force exerted by the defender on the ball is 75N. (\[-ve\]sign indicates that this force is opposite to the initial direction of the ball.)