Question

 

1) You can jump 3 m (10 feet) off of a diving board and into a swimming pool and be uninjured. However, if you jumped from the same height onto concrete it would be very bad. Use the principles of impulse and momentum to explain this.

2) A 125 kg linebacker running to the right at 2.5 m/s and an 80 kg quarterback running to the left at 3 m/s collide in midair. The linebacker holds on to the quarterback and they move off together. What is their velocity (magnitude and direction) after this collision?

Answer 1

1) If any person jumps from a certain height in a pool filled with water is not injured as compared to the person who jumps from the same height on the concrete this can be explain using impulse and momentum principle let's see how.

Suppose a man is jumping with velocity v1 and after hitting surface the final velocity i.e. v2 become zero. Now for any landing surface, the man's v1 will be same and v2=0.

So, the greater the stopping distance, the longer the time taken, so when a person lands on water the time taken to land completely is more as compared to landing on concrete.

Now, let's see this numerically. Acc to Newton 2nd law change in momentum with respect to time is equal to force.

P/t=F Where P is momentum

P= F*t

As we know momentum is mass*velocity, so it does not matter on which surface man is landing i.e. P will be same for all landings.

Now lets assume when man lands on water from 3 m height, because of some water properties the stopping time of man is increased and that resulted in less force or impact on man's body which causes no injury, whereas, when man landed on concrete surface, as concrete, in general, is hard so the stopping time is very less which exert high force on man's body which causes injury.

(2)