Question

A mis-hit golf ball flies straight upward. It reaches a height of 31.0 meters before falling back down. How fast was it going when it was hit? (Assume you can ignore drag)

Answer 1

v₀ = initial speed of the golf ball when it was hit = ?

v = final seed of the golf ball at the maximum height = 0 m/s

h = maximum height gained above the initial point = 31 m

m = mass of the golf ball

Using conservation of energy

initial kinetic energy just after being hit = final kinetic energy at maximum height + potential energy at the maximum height

(0.5) m v²₀ = (0.5) m v² + mgh

mass "m" cancel out so we get

(0.5) v²₀ = (0.5) v² + gh

inserting the values

(0.5) v²₀ = (0.5) (0)² + (9.8 x 31)

v²₀ = 303.8/(0.5)

v²₀ = 607.6

v₀ = sqrt(607.6 )

v₀ = 24.65 m/s