How Does Snow Impact Paratrooper Survival Physics?

[gschwarz]

Ive been trying to figure this out and i keep getting stuck.

A paratrooper pilot fell 380 m after jumping without his parachute opening. He landed in a snowbank, creating a crater 1.4 m deep, but survived with only minor injuries. Assume the pilot's mass was 76 kg and his terminal velocity was 50 m/s.

(a) Estimate the work done by the snow in bringing him to the rest.

(b) Estimate the average force exerted on him by the snow to stop him.

(c) Estimate the work done on him by the air resistance as he fell.


For part a i tried setting KE+GPE=W

so .5*76*50^2+76*9.8*380=W

I got 378024 J and it was incorrect. I don't know if some of my units are wrong or if my steps for solving part a are wrong.

Any help regarding parts b and c would be appreciated too.

The Attempt at a Solution

 

[Shooting Star]

In vacuum, you know what his KE at the point of hitting the ground should be. But it's less. Where's the deficit?

His KE + PE just before hitting the ground is known. In absence of snow, it should be same at any point. Again, how much is the deficit?

F_av = ma. If initial and final speeds are known, then a can be found, and thus F_av.

 

[ogb p]

:

First, let's make sure our units are consistent. The mass should be in kilograms (kg), velocity in meters per second (m/s), and height in meters (m). This will give us our answer in joules (J) for part a.

(a) To calculate the work done by the snow, we can use the equation W = Fd, where W is work, F is force, and d is displacement. In this case, the displacement is the depth of the crater, which is 1.4 meters. We can calculate the force by using the equation F = mg, where m is the mass (76 kg) and g is the acceleration due to gravity (9.8 m/s^2). This gives us a force of 745.6 N. Therefore, the work done by the snow is W = (745.6 N)(1.4 m) = 1043.84 J.

(b) To estimate the average force exerted on the pilot by the snow, we can use the same equation as before, F = mg. However, in this case, the force will be equal to the weight of the pilot, which is mg = (76 kg)(9.8 m/s^2) = 745.6 N. This means that the average force exerted on the pilot by the snow to stop him is 745.6 N.

(c) To estimate the work done on the pilot by air resistance, we can use the equation W = Fd, where F is the force of air resistance and d is the distance traveled. The distance traveled is the same as the height he fell (380 m). To calculate the force of air resistance, we can use the equation F = ½ρAv^2, where ρ is the density of air (1.2 kg/m^3), A is the cross-sectional area of the pilot (assuming he is in a standing position, this would be about 0.5 m^2), and v is the velocity (50 m/s). Plugging in these values, we get F = (0.5)(1.2 kg/m^3)(0.5 m^2)(50 m/s)^2 = 750 N. Therefore, the work done on the pilot by air resistance is W = (750 N)(380 m) = 285000 J.

It is important to note that these are all estimations and may not be completely