Question

a man of 80 kg.falls freelly from height1000m. upto 500m.he falls freely then retarding and reaches at earth with velocity 10m/ s .calculate work done by resistive force​

Answer 1

The journey is in 2 parts.

First part is free fall for 500 meters.

During first part,  

u = initial velocity = 0 m/sec

v = final velocity

a = g = 9.8 m/sec²

s = 500 meters

s = ut + at²/2

500 = 0 + 9.8*t²/2

t = √(5000/49) = 10√(50)/7 seconds

v = u + at = 0 + 9.8*10*√(50)/7 = 14(√(50)) m/sec

For the second part of the journey, man got retardation to reduce his speed when he reach ground.  

s = 500 meters

u = 14(√(50)) m/sec

v = 10 m/sec

v² – u² = 2as

a = (10*10 – 14*14*50)/2*500 = (100 – 9800)/1000 = -9.7 m/sec²

The retardation is 9.7 m/sec².

Work done = Force * distance = Mass * Acceleration * Distance = 80*9.7*500 = 388000 Jouls.

Work done by retarding force is 388000 jouls.