A parachutist bails out and freely falls 50 m. Then the parachute opens, and thereafter she deceler - ates at 2.0 m/s2. She reaches the ground with a speed of 3.0 m/s. (a) How long is the parachutist in the air? (b) At what height does the fall begin?

a) The parachutist in the air for 12.63 seconds.

b) The parachutist falls from a height of 293 meter.

Explanation:

Vertical motion of parachutist:

Initial speed, u = 0m/s

Acceleration, a = 9.81 m/s²

Displacement, s = 50 m

We have equation of motion, v² = u² + 2as

Substituting

v² = 0² + 2 x 9.81 x 50

v = 31.32 m/s

Time taken for this

31.32 = 0 + 9.81 x t

t = 3.19 s

After 50m we have

Initial speed, u = 31.32m/s

Acceleration, a = - 2 m/s²

Final speed, v = 3 m/s

We have equation of motion, v² = u² + 2as

Substituting

3² = 31.32² - 2 x 2 x s

s = 243 m

Time taken for this

3 = 31.32 - 2 x t

t = 9.44 s

a) Total time = 3.19 + 9.44 = 12.63 s

The parachutist in the air for 12.63 seconds.

b) Total height = 50 + 243 = 293 m

The parachutist falls from a height of 293 meter.