3. Two children are playing on a frozen lake by throwing different balls at a sm

Question

3. Two children are playing on a frozen lake by throwing different balls at a small ice block, The children throw sitting on top of the ice surface. The ice block has a mass of 10.0kg. a basketball, and a tennis ball at the initially stationary block. Then they slide the ice-block towards the stationary balls. (1) (10 points) If the children throw the 0.625kg-baskteball at 10.0 m/s, ind the ve- locity of ball and block after the collision. (Assume elastic.) (II) (10 points) If the children throw the 58.5g-tennis ball at 10.0/s. find the velocity of ball and block after the collision. (Assume elastic.) (II) (10 points) If the ice-block was thrown at 1.50 m/s, what speed each of the tw balls have after the collision, if they started at rest? (Assume elastic.)

Explanation / Answer

I) let m1 = 0.625 kg, u1 = 10 m/s

m2 = 10 kg, u2 = 0

let v1 and v2 are thevelocities of m1 and m2 after the collision.

v1 = (m1 - m2)*u1/(m1 + m2)

= (0.625 - 10)*10/(0.625 + 10)

= -8.82 m/s

v2 = 2*m1*u1/(m1 + m2)

= 2*0.625*10/(0.625 + 10)

= 1.18 m/s

II)

let m1 = 58.5 grams = 0.0585 kg, u1 = 10 m/s

m2 = 10 kg, u2 = 0

let v1 and v2 are thevelocities of m1 and m2 after the collision.

v1 = (m1 - m2)*u1/(m1 + m2)

= (0.0585 - 10)*10/(0.0585 + 10)

= -9.88 m/s

v2 = 2*m1*u1/(m1 + m2)

= 2*0.0585*10/(0.0585 + 10)

= 0.116 m/s

III)

speed of basket ball, v1 = 2*10*1.5/(10 + 0.685)

= 2.81 m/s

speed of tennis ball, v1 = 2*10*1.5/(10 + 0.0585)

=2.98 m/s

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