Question

A swimmer of mass 60 kg jumps from a height of 5 m in a swimming pool. When it comes in contact with the surface of water, its velocity becomes zero in 0.4 s. The average resistive force is ....... N

A. 2100
B. 2500
C. 1000
D. 1500

Answer 1

Hint: This question can be answered by using newton’s second law. According to Newton's second law for a particular system, rate of change of momentum will be equal to the external force acting on the system. Here external force will be due to the water on the man

Formula used:
${F_{ext}} = \dfrac{{d{p_{system}}}}{{dt}}$
$v = \sqrt {2gh} $

 Complete step by step answer:
When a person jumps from a certain height he will reach the ground with certain velocity and it is due to the law of conservation of mechanical energy. Total initial potential energy a man has will be converted into the kinetic energy by the time he reaches the surface of the water and from there water will do some work against the man to make the velocity of man to zero.
First we will find out the velocity gained by the man when he reaches the swimming pool.
It will be $v = \sqrt {2gh} $
Where ‘g’ is the acceleration due to gravity and ‘h’ is the height from the point where he jumps to the swimming pool
By taking ‘g’ as 10$m/{s^2}$ and ‘h’ as 5m we have
$v = \sqrt {2gh} $
$\eqalign{
  & \Rightarrow v = \sqrt {2 \times 10 \times 5} \cr
  & \Rightarrow v = \sqrt {100} \cr
  & \Rightarrow v = 10 \cr} $
Now this velocity became zero in 0.4 seconds. Hence the force opposite force acted to make this zero is
${F_{ext}} = \dfrac{{d{p_{system}}}}{{dt}}$
$\eqalign{
  & \Rightarrow {F_{ext}} = \dfrac{{m(0 - 10)}}{{0.4}} \cr
  & \Rightarrow {F_{ext}} = \dfrac{{60(0 - 10)}}{{0.4}} \cr
  & \Rightarrow {F_{ext}} = - 1500N \cr} $
Negative sign indicates that the force is opposing the downward motion
In addition to this the water must have compensated the effect due to weight too. So weight is $W = mg$
$\eqalign{
  & \Rightarrow W = 60 \times 10 \cr
  & \Rightarrow W = 600N \cr} $
So in total the amount of opposing force given by water is $1500 + 600 = 2100N$
Hence answer would be option A

Note:
In the question they asked about the average force but not the actual force because the force exerted by the water is not constant and it varies so we can find the actual value of force and we can find average value only, more over work has to be done by water to resist the existing kinetic energy when man reached water and to resist the kinetic energy which is going to be created further due to weight and hence we added magnitude of weight to the resisting force.