Suppose a 0.370 kg ball is thrown at 14.0 m/s to a motionless person standing on

Question

Suppose a 0.370 kg ball is thrown at 14.0 m/s to a motionless person standing on ice who catches it with an outstretched arm as shown in the figure below. (a) Calculate the final linear velocity (in m/s) of the person, given his mass is 67.0 kg. m/s (b) What is his angular velocity (in rad/s) if each arm is 7.00 kg? You may treat the ball as a point mass and treat the person's arms as uniform rods (each has a length of 0.910 m) and the rest of his body as a uniform cylinder of radius 0.150 m. Neglect the effect of the ball on his center of mass so that his center of mass remains in his geometrical center. rad/s

Explanation / Answer

a] using momentum conservation,

(M+m)v = mu

v = mu/(M+m)

v = 0.370*14/(67.370)

= 0.07689 m/s answer

b) By conservation of angular momentum about axis of cylinderical man,

mu (r+L) = i w

0.370*14*(0.15+0.91) = (2*(1/3*7*0.91^2+7*0.15^2) + 0.5*(67-2*7)*0.15^2 + 0.37*(0.15+0.91)^2) w

5.4908 = 5.1914w

w = 5.4908/5.1914

= 1.06 rad/s answer

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