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Question

A healthy young man stand at a distance of 7m from a 11.8mheight building sees a kid slipping from the top floor. With what speed (assume uniform) should he run to catch the kid at the arm s height at 1.8m


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Solution

Step 1. Given data

A healthy young man stand at a distance of 7m.

The height of the building is 11.8m.

The kid should caught over 1.8m from the ground level.

Initial velocity is 0m/s

Step 2. Formula used

Speed =st

where s is the distance and t is the time

Equation of the motion

s=ut+12gt2

where sis the distance , u the initial velocity gis the gravitational constant.(take g=9.8m/s2) and t is the time.

Step 3. Find the distance traveled by the kid

The distance covered by the kid before he was caught is =11.8-1.8=10m

Step 4. Find the time taken to fall

Let the time taken to fall is t

s=10mg=9.8m/s2u=0m/s

The equation of the motion is

s=ut+12gt210=0+12×9.8×t2t2=2.04t=1.42s

Step 5. Find the speed at which the man ran

The speed at which the man ran in order to catch the kid is

Speed=st

=71.42=4.9m/s

Hence, the man ran at a speed of 4.9m/s.


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