Jesse and Mary go to a carnival, and Jesse is determined to win Mary an oversize

Question

Jesse and Mary go to a carnival, and Jesse is determined to win Mary an oversized stuffed animal. The game he goes to has 0.25 kg ball, which he is supposed to throw at a 10 kg block that is hanging from a 3 m long connected to the sealing. If Jesse is able to throw the ball and hit the block, making it swing up and hit the ceiling, then he wins the animal. Mary convinces Jesse that he should cheat, and use a rubber ball that looks and had the same mass as the regular ball, but the collisions are virtually elastic (very little kinetic energy is lost How fast does Jesse have to throw the rubber ball to win the animal?

Explanation / Answer

If the large mass has to hit the ceiling all its initial kinetic energy is transformed into potential energy at the minimum speed

MV^2/2 = Mgh

V = sqrt(2gh) =sqrt(2*9.81*3) =7.672 m/s

Since the colision is elastic the total momentul and energy is conserved

mV0^2/2 = MV^2/2 +mV1^2/2

mV0 =MV +mV1

m(V0-V1) =M*V

and m(V0-V1)(V0+V1) = MV^2

V0-V1 = M/m* V = 10/0.25*7.672 =306.88 m/s

V0+V1 =V/2 =7.672 m/s

adding we get

2V0 =310.716 m/s

V0 =157.276 m/s

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