A Rugby player kicks a ball by standing and rotating his kicking limb about the

Question

A Rugby player kicks a ball by standing and rotating his kicking limb about the hip, keeping the knee and ankle rigid. Starting when his kicking limb is rotating clockwise at 350degrees/second, he accelerates the limb counterclockwise at a constant 2800 degrees/ second^2 until his foot impacts the ball. During this period of acceleration prior to ball impact, his limb undergoes a counterclockwise angular displacement of 55 degrees. The kicking foot impacts the ball at a point 120 cm from the hip.

a) What is the magnitude of the angular velocity of the player's kicking limb at the instant of ball impact?

b) At the intant of ball impact, what is the magnitude of the linear velocity of the player's kicking foot at the point of impact?

Please show the step by step process you used to get the answer. Thanks in advance!!

Explanation / Answer

Initial angular velocity = 350 degrees/sec = 6.11 rad/sec

angular acceleration = 2800 degrees/s^2 = 48.87 rad/s^2

angular displacement = 55 degrees = 0.96 rad

hence final angular velocity = sqrt(omega_0^2+2alpha*theta) = sqrt(6.11^2+2*48.87*0.96) = 11.45 rad/s

linear velocity = omega *r = 11.45*120/100 = 13.74 m/s

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