Question

When a golfer tees off, the head of her golf club which has a mass of 158 g is traveling 48.2 m/s just before it strikes a 46.0 g golf ball at rest on a tee. Immediately after the collision, the club head continues to travel in the same direction but at a reduced speed of 32.7 m/s. Neglect the mass of the club handle and determine the speed of the golf ball just after impact.

Answer 1

v₂ = 53.23 m/s

Step-by-step explanation:

Given that,

The mass of a golf club, m₁ = 158 g = 0.158 kg

The initial speed of a golf club, u₁ = 48.2 m/s

The mass of a golf ball, m₂ = 46 g = 0.046 kg

It was at rest, u₂ = 0

Immediately after the collision, the club head continues to travel in the same direction but at a reduced speed of 32.7 m/s, v₁ = 32.7 m/s

We use the conservation of energy to find the speed of the golf ball just after impact as follows :

`m_1u_1+m_2u_2=m_1v_1+m_2v_2\\\\v_2=(m_1u_1-m_1v_1)/(m_2)\\\\v_2=(0.158(48.2)-0.158(32.7))/(0.046)\\\\=53.23\ m/s`

So, the speed of the golf ball just after the impact is equal to 53.23 m/s.