How much work has to be done on a moving ball to get it to switch directions?

Question

A 15 g plastic ball is moving to the left at 45 m/s. How much work must be done on the ball to cause it to move to the right at 45 m/s?

Answer 1

to stop the ball Energy required is 15.1875 J

to make the ball role in reverse direction energy required is

                                                             15.875J

Total energy required = 30.375 J

Answer 2

Work is the energy you put into the system. We're going to assume no energy is lost to friction or sound or anything like that.

Initially the ball has K = 1/2*m*v^2 = -15.1875J of kinetic energy (it's negative because it's moving to the left).

Therefore we need to put in 15.1875J of energy to get it to stop and then another 15.1875J of energy to get it moving at +45 m/s

Therefore our answer is 30.375J of work done.