Question

1. If a sky-diver jumps out of a plane, two forces will act on him, gravity and air resistance. If we assume air resistance is proportional to the velocity, we get the total force on the sky diver will be F = −gm − kv, where g is a acceleration due to gravity on the surface of the earth, m is the mass of the sky-diver, v is the velocity of the sky-diver, and k is constant of proportionality for wind resistance. In this situation, we have that the height of the sky-diver will be given by the equation, s(t) = c1e −k m t − gm k t + c2 where c1, c2 are constants. Suppose that the sky-diver is 100kg, the force due to gravity is 10m/sec2 and k = 20kg/sec. Then, complete the following.

(i) Find v(t) and a(t).

(ii) For the a(t) you got, check that m ∗ a(t) is equal to the force given by first equation if.

(iii) Suppose v(0) = 0m/sec and s(0) = 3000 m. Use this to solve for c1 and c2. Give a function for height in terms of time (fill in numbers for all constants).

(iv) When the sky diver hits the ground (that is before he feels the eWhen the sky diver hits the ground (that is before he feels the effects of the landing), what will be his height, velocity and acceleration?

I NEED IV

Answer 1