Question

A ball is dropped from a height of 5m into a sandy floor and penetrates 10cm find retardation

Answer 1

Use the equations of motion:
v2-u2 = 2as
Final vel = v = 0
Initial vel = u = √(2g*5) = √(10g)------ {this is obtained by initial vel=0 as droped from a ht, final vel is what u have to determine, height s = 5 mt and accn due to gvt = g, so u2-0=2*g*h or u=√(2gh)}

So 0-10g = 2(a)*(10/100)
So a = -50g.

So retardation is 50*g = 500ms-2.

Hope that helps.