27. if you throw a 1.0 kg ball straight up at 40 m/s off the ground, what is its velocity at the highest point? use
conservation of energy to determine how high does the ball go?

The height of the ball, h = 81.63 m

The velocity of the ball at the highest point is zero

Explanation:

Given data,

The mass of the ball, m = 1 kg

The initial velocity of the ball, u = 40 m/s

Using the conservation of energy, the total mechanical energy of the ball initially at u = 40 m/s

              E = P.E + K.E

               E = 0 + ½ mv²

                   = ½ x 1 x 40²

                   = 800 J

The maximum height the ball reaches with the energy E = 20 J

The K.E of the ball is zero at the maximum height

                      E = mgh

                       h = E / mg

                          = 800 / (1 x 9.8)

                           = 81.63 m

The height of the ball, h = 81.63 m

The velocity of the ball at the highest point is zero.