Consider the following statement:
When jumping from some height, you should bend your knees as you come to rest, instead of keeping your legs stiff. Which of the following relations can be useful in explaining the statement.
A.$\Delta \overrightarrow{{{P}_{1}}}=-\Delta \overrightarrow{{{P}_{2}}}$
B.$\Delta E=-\Delta (PE+KE)=0$
C.$\overrightarrow{{{F}_{1}}}\Delta t=m\Delta \overrightarrow{v}$
D.$\Delta \overrightarrow{x}$ $\alpha $ $\Delta \overrightarrow{F}$

Hint:When jumping from some height, we should bend our knees once we come to rest. Because the change of momentum is equal to the impulse, which is force times the time. Hence a higher time means less force when coming to rest. So, by bending our knees we can avoid hurting our legs, increasing the time of landing, and decreasing the momentum.




Complete answer:
While jumping from some height, we can be seriously injured if we keep our legs stiff. To avoid this kind of injury is to bend our knees upon landing to reduce the force of the impact. This is because it slows the change of momentum of our body with time. Hence our body applies less force on the ground and the respective ground applies less amount of force in return.
We know the impulse is the product of force ($F$) and the time interaction of force ($\Delta t$) is equal to the change of momentum.
Impulse $=F\times \Delta \overrightarrow{t}$
The change in momentum$=m\times \Delta \overrightarrow{v}$
Therefore, $F\times \Delta \overrightarrow{t}=m\times \Delta \overrightarrow{v}$
During the jumping impact of force can be reduced by increasing time which can be increased by bending our knees.
Thus, option (C) is correct.










Note:During the catching of a fast-moving ball with our hands then we are trying to stop the motion of the ball. But when we keep our hand stationary, this exerted force with momentum transferred might hurt our hand, that’s why we should lower our hand while catching the fast-moving ball. So catching time increases and decreases the momentum.