Calculating Diver Momentum & Force in Acapulco | Physics Homework

[crosbykins]

Homework Statement

Divers at Acapulco, Mexico, regularly dive head first from a heigh of 36m into water 3.6m deep. [assuming g=9.8m/s^2) and that air resistance is negligible.]
a) What would be the vertical momentum of a 50kg diver when he reached the water?
b)If he lost his vertial velocity by the time he reached a depth of 3.0, what average force must the water exert on him?
c)Comment on the likely results if the inital force as he entered the water was ten times the averag force.
d)The rocks at the base of the cliff jut more than 6m out into the water. If a diver hit these would he be killed. Why?

*****need help with c) and d)

Homework Equations

p=mv
Ft=m(change in v)
p0=pf

The Attempt at a Solution

honestly, I have no idea...if his inital force was 10X the average force...does this mean he hits the water will 10x the force that the water pushes back up on him...so, he travels downward more...it takes more time for his velocity to come to a rest...so therefore, the average force has less of an impact on him...for d)...he will be killed if he hits the rocks b/c since they are hard&have less SA than the water, he will be in contact with them for less time...so there will be a greater average force exerted on him and he is killed...

 

[anathema]

a) The vertical momentum of the diver can be calculated using the equation p=mv, where p is the momentum, m is the mass of the diver (50kg), and v is the velocity. At the moment of impact, the diver's velocity will be equal to the velocity due to gravity, which can be calculated using the equation v^2=u^2+2as, where u is the initial velocity (0), a is the acceleration due to gravity (9.8m/s^2), and s is the distance traveled (36m). Plugging in the values, we get v=24.6m/s. Therefore, the vertical momentum of the diver will be p=(50kg)(24.6m/s)=1230kgm/s.

b) The average force exerted on the diver by the water can be calculated using the equation Ft=m(change in v), where Ft is the average force, m is the mass of the diver, and change in v is the change in velocity. In this case, the change in velocity is equal to the initial velocity (24.6m/s), since the diver loses all of his vertical velocity by the time he reaches a depth of 3.0m. Therefore, the average force will be Ft=(50kg)(24.6m/s)=1230N.

c) If the initial force as he entered the water was ten times the average force, this means that the diver would hit the water with a much higher velocity, since the force acting on him is greater. This would result in a longer time for the diver to come to a stop, and therefore, a smaller average force exerted on him by the water. However, the impact force on his body would be much greater, which could potentially cause injury or harm. The likelihood of this would depend on various factors, such as the angle of entry and the physical condition of the diver.

d) If the diver hit the rocks at the base of the cliff, he would most likely be killed due to the impact force exerted on his body. This is because rocks are much harder and have less surface area compared to water, so the force acting on the diver's body would be much greater. Additionally, the time of impact would be shorter, resulting in a higher average force exerted on the diver. This could cause severe injuries or even death. Therefore, it is important for divers to be aware of their surroundings and to always