A parachutist after bailing out falls 50m without friction. When parachute opens, it decelerates at `2m//s^2`. He reaches the ground with a speed of `3m//s`. At what height, did the bail out?

Options

A. 91 m
B. 182 m
C. 293 m
D. 111 m

Answer

C

Explanation

Paracute bails out at height `H` from ground.
Velocity at `A`
`v = sqrt(2 gh)`
=`sqrt(2 xx 9.8 xx 50)`
=`sqrt(980) m//s`
The velocity at ground `v_1 = 3 m//s` (given)
Acceleration `= -2 m//s^2` (given)
`:. H - h = (v^2 - v_1^2)/(2 xx 2)`
=`(980 - 9)/(4)`
=`(971)/(4) = 242.75`
`:. H = 245.75 + h`
=`242.75 + 50 ~~ 293 m`.