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/s²,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 .
b) 5 m .
c) 25 m .
d) 10 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.

      V_o = 10 m/s       , V_f = 0 m/s.

Consider the following differential equation in which a, v and s represent the acceleration, velocity and displacement respectively.

Substituting the values of the initial and final velocities we get,

   ( 0 - 10²) /2 = - 2( s²)
   s² = 25
   s = 5 m.

The depth of the lake is 5 m.