A 50g ball is fired horizontally with initial speed v 0toward a 100g ball that i

Question

A 50g ball is fired horizontally with initial speed v0toward a 100g ball that is hanging motionless from a 1.1m -long string. The balls undergo a head-on, perfectly elastic collision, after which the 100g ball swings out to a maximum angle ?max = 52?.

Part A

What was v0?

A 50g ball is fired horizontally with initial speed v0toward a 100g ball that is hanging motionless from a 1.1m -long string. The balls undergo a head-on, perfectly elastic collision, after which the 100g ball swings out to a maximum angle ?max = 52?.

Part A

What was v0?

Explanation / Answer

By conservation of energy, if v2f = the final velocity of the 100 g ball,

1/2 m vf^2 = m g L (1 - cos 52)

Solving for vf,

vf = 2.8786 m/s

Thus, by conservation of energy and momentum on their collision (As the collision is perfectly elastic), the initial velocity of the 50 g ball is

vo = 4.3179 m/s   [ANSWER]

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