What is the minimum depth of snow needed to stop a paratrooper safely?

[patelkey]

Homework Statement

A paratrooper fell 375 m from an airplane without being able to open his chute. Assume that his speed at impact was 52 m/s (terminal speed), that his mass (including gear) was 85 kg, and that the force on him from the snow was at the survivable limit of 1.2 multiplied by 105 N.

a.) What is the minimum depth of snow that would have stopped him safely?

b.)What is the magnitude of the impulse on him from the snow?

Homework Equations

The Attempt at a Solution

 

[rl.bhat]

Hi patelkey, welcome to PF. Please go through the PF rules. According that you have to show how much you know about the problem. You have to find out the relevant equations to solve the given problem. You have to your attempts. Still you are not getting the answer, we will help you.
So first of write down the relevant equations.

 

[tomcue]

a.) To determine the minimum depth of snow needed to stop the paratrooper safely, we can use the equation for kinetic energy, KE = 1/2mv^2, where m is the mass of the paratrooper and v is his speed at impact. Since the force of the snow on the paratrooper is equal to the change in momentum, we can also use the equation FΔt = mΔv, where F is the force of the snow, Δt is the time interval of impact, and Δv is the change in velocity. By setting these two equations equal to each other, we can solve for the minimum depth of snow, d, using the equation d = (mΔv)/(2F). Plugging in the given values, we get d = (85 kg * 52 m/s)/(2 * 1.2 * 105 N) = 1.48 m. Therefore, the minimum depth of snow needed to stop the paratrooper safely is approximately 1.48 meters.

b.) The impulse on the paratrooper from the snow can be calculated using the equation Impulse = FΔt, where F is the force of the snow and Δt is the time interval of impact. Plugging in the given values, we get Impulse = (1.2 * 105 N)(Δt). Since we do not know the exact time interval of impact, we cannot calculate the exact magnitude of the impulse. However, we can say that the magnitude of the impulse would be equal to or less than 1.2 * 105 N.