A punter kicks a football by generating a hip flex ion angular velocity of 30 ra

Question

A punter kicks a football by generating a hip flex ion angular velocity of 30 rad/s k. At the time the punter's foot contacts the ball, the displacement of the foot relative to the hip is defined as r= 0.7i - 0.5j meters. Assuming that the ball leaves the foot with the same linear velocity that the foot had at the time of contact, and that the ball is kicked and fielded at the same height, 1 meter, determine the following:

a. The linear velocity of the ball as it leaves the foot.

b. The time taken for the ball to achieve its peak height.

c. The maximum height achieved by the punted ball.

d. The distance, in yard, that the punt traveled down the field.

Explanation / Answer

v = r X w = (0.7 i -0.5 j) X 30 k = (-21 j - 15 i )

So magnitude of linear velocity is v = sqrt(21^2+15^2) = 25.8 m/s

B) t = u/g = (25.8)/9.81 = 2.62 s

C) Hmax = u^2/(2*g) = (25.8^2)/(2*9.81) = 33.92 m

D) after t sec

x = (-15*2.62) = -39.3 m

y = (-21*2.62)= -55.02 m

final position is r2 = (-39.3-0.7) i +( -55.02-0.5) j = -40 i - 55.52 j

magnitude of dispalcement is sqrt(40^2+55.52^2) = 68.42 m

So the distance is 68.42 - sqrt(0.7^2+0.5^2) = 67.55 m

in yard 67.55 m = 73.87 yard

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