Aman of mass 80kg stands next to a stationary ball of mass 4kg on a frictionless surface. he kicks the ball forward along the surface with a speed 15m/s. calculate the man’s recoil speed.

According to the conservation of momentum.  In this situation, the initial momentum is equal to zero.

Since,
p=mv (Momentum)

The initial velocity of the ball = 0 m/s
The initial velocity of the man = 0 m/s

Therefore,
Total Momentum  = 0
 Law of Conservation of momentum states that the vector sum of the final momenta must be equal to zero which means they will have the same magnitude but in opposite directions.

When the ball is kicked forward along the surface with a speed 15 m/s. 
then the momentum will be:

p = 4 x 15 = 60 kgm/s.
Now, the momentum of the man can be calculated as:
p = 60 kgm/s
mv = 60 kgm/s
As,
mass of the man = 80kg
So,
80 × v = 60 kgm/s
v = 60÷80
v = 0.75 m/s

0 = 0.40 / 0 = 0

= 0.20 = 9.80 ⁄2 =?

=0 , = = 0.20 =0.50 0 0.40 ⁄

=0−122 =0−12(9.80 ⁄2)(0.50)2 =1.2

Your answer is 120miles