Question

A parachutist jumps from height 100 m. 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 after the parachute propeller is switched on total acceleration of the man varies with velocity as a = –2v, where v is the instantaneous velocity of the man. Find the time after falling freely man should switch on parachute propeller for this purpose. (Use g = 10m/s^2).

Answer 1

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$\huge\tt{SOLUTION:}$

As,dv/dt = -2v

v(t) will be an exponential function, so it will never be zero.

Anyways, consider that after falling for k seconds,

v = -9.8k

so, after t more seconds when s = 0, we want v close to zero

➠v = -9.8k e^(-2t)

➠s = 100 - 9.8kt + 1/2 at^2

➠1000 - 9.8kt - 9.8k×e^(-2t)×t^2

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Answer 2

Answer:

A parachutist jumps from height 100 m

a parashutist jumps from height 100 m. He wants to reach at ground with zero velocity. For this purpose he switches on a parachute propeller after falling freely for certain height.

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