# A body is released from a height of 100 m falls freely. What is the time taken by the body to fall 10 and 20 meters? (Take g = 10m/s^2)

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The body is released from a height of 100 m and falls freely. The acceleration on the body is due to gravity and equal to 10 m/s and its initial velocity is 0 m/s.

Now we use the relation y = ut + (1/2) a*t^2 to find the time taken to travel 10 m and 20 m.

For 10 m:

y = ut + (1/2) a*t^2

=> 10 = 0*t + (1/2)*10*t^2

=> 10 = 5t^2

=> t^2 = 2

=> t= sqrt 2 s.

For 20 m:

y = ut + (1/2) a*t^2

=> 20 = 0*t + (1/2)*10*t^2

=> 20 = 5t^2

=> t^2 = 4

=> t= 2 s.

**Therefore we see that the body takes sqrt 2 s to fall 10 m and 2 s to fall 20m.** The time taken to travel 20 m is not twice that taken to travel 10 m as the body is accelerating.