(a) A 59.3 g tennis ball is moving at -14.5 m/s when it collides elastically and

Question

(a) A 59.3 g tennis ball is moving at -14.5 m/s when it collides elastically and head-on with a heavier ball moving in the opposite direction at +9.62 m/s. The tennis ball rebounds at twice its initial speed. Find the mass of the heavier ball.

(b) The Pirate Club has readied a 4.1 m long jollyboat for launching. The captain and the officer plan to carry the loot of their pillaging to a secret location to bury it.The craft requires balancing such that the center of mass of cargo and crew is directly amidships. They have a 19 kg treasure chest mounted 1.2 m from the prow of the raft . The 57 kg bosun will stand 0.3 m from the stern to steer the craft. How far from the prow should the 82 kg captain stand in order to balance the jollyboat and keep from losing their treasure?

Explanation / Answer

given that

m1 = 59.3 kg

u1 = -14.5 m/sec

m2 = ?

u2 = 9.62 m/sec

v1 = 2*14.5 = 29 m/sec

since this is a elastic collision

using law of conservation of momentum

(m1*u1)+(m2*u2) = (m1*v1)+(m2*v2)

(-59.3*14.5)+(m2*9.62) = (59.3*29)+(m2*v2)

(m2*v2)-(m2*9.62) = -2579.55

m2*(v2-9.62) = -2579.55

also using law of conservation of kinetic energy

(0.5*m1*u1^2)+(0.5*m2*u2^2) = (0.5*m1*v1^2)+(0.5*m2*v2^2)

(0.5*59.3*14.5^2)+(0.5*m2*9.62^2) = (0.5*59.3*29^2)+(0.5*m2*v2^2)

-18701.73 = 0.5*m2*(v2^2 - 9.62^2)

-18701.73 = 0.5*m2*(v2+9.62)*(v2-9.62)

but m2*(v2-9.62) = -2579.55

-18701.73 = 0.5*(-2579.55)*(v2+9.62)

v2 = 4.88 m/sec

and m2*(v2-9.62) = -2579.55

m2*(4.88-9.62) = -2579.55

m2 = 544.2 g

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