Question

# A goalkeeper in a game of football pulls his hands backward after holding the ball shot at the goal. This enables the goalkeeper to

A

Exert larger force on the ball

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B

Reduce the force exerted by the ball on the hands

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C

Increase the rate of change in momentum

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D

Decrease the rate of change in momentum

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Solution

## The correct option is D Decrease the rate of change in momentumThe explanation for the correct optionOption $B$and Option $D$After holding the ball, the goalkeeper pulls his hands backward to slow down the rate of change of momentum while increasing the time.The force is directly related to the rate of change of momentum, this allows less force to be exerted on his hands if he moves his hands backward.According to newton's second law, the rate of change of momentum of a body is equal to the force applied to the body.From newton's second law Rate of change of momentum$=\frac{d\left(mv-mu\right)}{dt}$$m=Massofthebody\phantom{\rule{0ex}{0ex}}u=Initialvelocityofthebody\phantom{\rule{0ex}{0ex}}v=Finalvelocityofthebody$$=m·\frac{d\left(v-u\right)}{dt}\phantom{\rule{0ex}{0ex}}=m·a\left[\because Acceleration\left(a\right)=\frac{d\left(v-u\right)}{dt}\right]\phantom{\rule{0ex}{0ex}}=force$From the above derivation, we can see that if we increase the time of ball travel the rate of change in momentum of the ball decreases which results in a decrease in the force of the ball.Hence, the correct options are $B$ and $D$.

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