Question

A body of mass 20kg falls from rest through a height of 10m and comes to rest having penerated a distance of 9.8m into sandy ground calculate the average force exerted by the sand in bringing the body to rest(take g=10m/s^2)
get crash speed
(1/2) m v^2 = m g h
v = sqrt (2 g h) (but you knew that, right?)
v = sqrt (2*9.81*10) = 14 meters/second
momentum at crash = m v = 20 * 14 = 280 kg m/s
calculate time to stop
average stop speed = 7 m/s
stop distance = 9.8 meters
t = stop time = 9.8 m / 7 m/s = 1.4 seconds
average force = change of momentum / time to stop = 280 /1.4 = 200 Newtons

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