High-speed stroboscopic photographs show that the head of a 184 g golf club is traveling at 35.2 m/s just before it strikes a 45.9 g golf ball at rest on a tee. After the collision, the club...

 

High-speed stroboscopic photographs show that the head of a 184 g golf club is traveling at 35.2 m/s just before it strikes a 45.9 g golf ball at rest on a tee. After the collision, the club head travels (in the same direction) at 22.7 m/s. Find the speed of the golf ball immediately after impact.

 

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justaguide | College Teacher | (Level 2) Distinguished Educator

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High-speed stroboscopic photographs show that the head of a 184 g golf club is traveling at 35.2 m/s just before it strikes a 45.9 g golf ball at rest on a tee. After the collision, the club head travels (in the same direction) at 22.7 m/s. The speed of the golf ball immediately after impact has to be determined.

The law of conservation of momentum states that the total momentum of the system which in this problem consists of the golf club and the golf ball remains the same. The initial momentum is equal to the final momentum.

Initially, the golf ball is stationary and the club is moving at 35.2 m/s. The total momentum of the system is 0.184*35.2 + 45.9*0 =  6.4768 kg*m/s.

After collision let the speed of the ball be v. As the speed of the club is 22.7 m/s, the total momentum is 0.0459*v + 0.184*22.7 = 0.0459*v + 4.1768

Equating the initial and final momentum 0.0459*v + 4.1768 = 6.4768

=> 0.0459*v = 6.4768 - 4.1768

=> v = 50.10 m/s

The velocity of the golf ball immediately after collision is 50.10 m/s.

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