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 , Vo, 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 Vf, is zero.

      Vo = 10 m/s       , Vf = 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.