Question

A parachutist jumps from height 100m. He wants to reach at ground with zero velocity. For this purpose he switches on a parachute propeller after falling freely for certain height. Given that the parachute propeller is switched on total acceleration of the man varies with velocity as a = -2v, where v is instantaneous velocity of the man. Find the time after falling freely man should switch on parachute propeller for this purpose.

Answer 1

since dv/dt = -2v
v(t) will be an exponential function, so it will never be zero. You sure you don't want to specify some small acceptable speed at touchdown?

Anyway, consider that after falling for k seconds,

v = -9.8k
and after t more seconds when s=0, you want v close to zero

v = -9.8k e^(-2t)
s = 100 - 9.8kt + 1/2 at^2
= 100 - 9.8kt - 9.8k*e^(-2t)*t^2

See what you can do with that.

Answer 2

Can't you make it little easier ? We asked this question so that we can solve this difficult question but this solution is more difficult than the question itself.

Answer 3

Retry