Final answer:
The speed of the golf ball just after impact, calculated using the conservation of momentum, is approximately 20.87 m/s. This result is derived from the initial and final velocities of the golf club and the initial velocity and mass of the golf ball.
Step-by-step explanation:
The question involves a collision between a golf club and a golf ball and asks to determine the speed of the golf ball just after impact. This is a classic example of a conservation of momentum problem. Since no external forces are acting on the system, the total momentum before the collision is equal to the total momentum after the collision. The formula for the conservation of linear momentum in a two-object system is m1×u1 + m2×u2 = m1×v1 + m2×v2.
We are given the following information:
Initial speed of the golf club (u1) = 50 m/s
Mass of the golf club (m1) = 160 g = 0.160 kg (since 1g = 0.001 kg)
Initial speed of the golf ball (u2) = 0 m/s (at rest)
Mass of the golf ball (m2) = 46 g = 0.046 kg
Final speed of the golf club (v1) = 44 m/s
Applying conservation of momentum:
0.160 kg × 50 m/s + 0.046 kg × 0 m/s = 0.160 kg × 44 m/s + 0.046 kg × v2
Solving for v2 (the speed of the golf ball after collision):
8 kg×m/s = 7.04 kg×m/s + 0.046 kg × v2
0.046 kg × v2 = 8 kg×m/s - 7.04 kg×m/s
0.046 kg × v2 = 0.96 kg×m/s
v2 = 0.96 kg×m/s / 0.046 kg
v2 = 20.87 m/s
Therefore, the speed of the golf ball just after impact is approximately 20.87 m/s.