Question

High-speed stroboscopic photographs show that the head of a 260-g golf club is traveling at 51 m/s just before it strikes a 46-g golf ball at rest on a tee. After the collision, the club head travels (in the same direction) at 38 m/s. Find the speed of the golf ball just after impact.

Answer 1

The concept necessary to solve this problem is linked to the conservation of momentum, for which it is established that the initial momentum must be equal to the final momentum. Therefore, the product between the initial speeds times the mass will be equal to the product of the final speeds times the mass, therefore we have that our values are:

$\text{Mass of golf club head} = M = 260 g = 0.26kg$

$\text{Initial Velocity of this ball} = 51m/s$

$\text{Mass of golf ball on tree} = m = 46g = 0.046kg$

$\text{Initial velocity of this ball} = u_2 = 0m/s$

After collision we have,

$\text{Velocity of the club head golf ball} = v_1 = 38m/s$

$\text{Velocity of the golf ball after the collision} = v_2 = ?$

From conservation of linear momentum,

$Mu_1 + mu_2 = Mv_1+mv_2$

Rearranging to find the velocity 2,

$v_2 = \frac{(Mu_1 + mu_2)-Mv_1}{m}$

$v_2 = \frac{(0.26*51 + 0.046*0)-0.26*38}{0.046}$

Replacing,

$v_2 = 73.47m/s$

Therefore the speed of the golf ball just after impact is 73.47m/s