A ball is dropped from a hieght of 5m onto a Sandy floor and penetrates the sand upto 10 cm before coming to rest . Find the retardation of the ball in sand assuming it to be uniform.

Initial velocity(u) of the ball is 0 m/s.

Let the final velocity of the ball when it just strikes the sand is v m/s.

Applying Newton's laws,we get,

v²-u²=2gs

v²-0=2(10)(5)

v²=100

v=10 m/s.

Now, initial velocity(v) when the ball strikes the sand is 10 m/s

and the final velocity v' when the ball stops inside the sand is 0 m/s.

Here,displacement inside the sand is 10 cm or 0.1 m

and the accn. of the ball inside the sand is a' m/s².

again,applying Newton's laws,we get,

v'²-v²=2a's

0-100=2(-a)(0.1).........(here the negative sign indicates retardation of the ball,i.e.negative acc. of the ball.)

-100=-0.2a

a=500m/s²

So,the retardation of the ball is 500m/s².