Later that same day, you and your family go turkey bowling. Your little brother,

Question

Later that same day, you and your family go turkey bowling. Your little brother, an up- and coming turkey bowling prodigy, knocks all of the pins but one down on the first bowl. On the second, he hurtles his frozen turkey straight down the lane and strikes the remaining pin slightly off-center. Taking “down the lane” to be east, after the collision the turkey continues moving at 8.5 m/s at an angle 3 degrees north of east, and the pin flie t an angle 3 degrees north of east, and the pin flies away at 20 m/s. At what angle (south of east) does the pin move? What is the initial speed of the turkey (prior to the collision)? Assume the pin and the turkey have the same mass of 10 kg and the owner of the alley invested in a frictionless lane for the occasion.

Explanation / Answer

M = mass of turkey = mass of pin = 10 kg

Vix = initial velocity of turkey in X-direction or east direction = ?

vix = initial velocity of pin = 0 m/s

vfx = final velocity of pin along x-direction = 20 costheta

Vfx = final velocity of turkey along x-direction = 8.5 Cos3

using conservation of momentum along x-direction

MVix + M vix = M Vfx + m vfx

Vix + 0 = (8.5 Cos3) + 20 costheta eq-1

Along the Y-direction

Viy = initial velocity of turkey in Y-direction = 0

viy = initial velocity of pin = 0 m/s

vfy = final velocity of pin along Y-direction = - 20 Sintheta

Vfy = final velocity of turkey along Y-direction = 8.5 Sin3

using conservation of momentum along x-direction

MViy + M viy = M Vfy + m vfy

0 + 0 = (8.5 Sin3) + 20 Sintheta

theta = 1.27 deg

using eq-1

Vix + 0 = (8.5 Cos3) + 20 costheta

Vix  = (8.5 Cos3) + 20 cos1.27 = 28.5 m/s

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