A person wants to find the depth of a lake. He shoots a spherical object vertically downwards and it strikes the surface of water with a velocity of 10 m / s. Due to resistance of water, the spherical object experiences a deceleration given by the equation a =  (4s) m/s^{2},where s is the displacement ( in meters) measured from the surface of the water. The object just manages to touch the floor of the lake before moving upwards. Find the depth of the lake. a) 7 m . 

The initial velocity
, V_{o}, is 10 m / s and since it is given that the object just
manages to touch the floor of the lake, its velocity when it touches the
floor of lake, say V_{f}, is zero.
Substituting the values of the initial and final velocities we get, (
0  10^{2}) /2 =  2( s^{2}) The depth of the lake is 5 m. 