8. A rugby ball has a mass of 0.5 kg. Initially it is moving in the -x-direction

Question

8. A rugby ball has a mass of 0.5 kg. Initially it is moving in the -x-direction at speed of 5 m/s, but then it is kicked with an average net force r. After the kick the ball is moving at an angle 50 degrees upward and to the right with a speed of 55 m/s. A) Find the impulse vector J. B) Find the average net force vector F. C) What is the angle beta that the net force vector D make with respect to the +x-axis? D) State the j necessary condition for the angle beta to be identical to the angle alpha. E) Prove that this condition results in beta and a being equivalent. You may assume a collision time of delta t = 0.01 s.

Explanation / Answer

Here ,

mass , m = 0.5 Kg

initial velocity , u = -5 i m/s

final velocity , v = 55 *(cos(50) i + j * sin(50)) m/s

v = 35.4 i + j * 42.12 j m/s

A) impulse = mass * change in velocity

impulse = 0.5 *(35.4 i + j * 42.12 j - (-5 i))

impulse = 0.5 *(39.4 i + 42.12 j ) N.s

impulse = 19.7 i + 21.1 j

the impulse vector J is 19.7 i + 21.1 j

B)

the net force is Fnet

Fnet = (19.7 i + 21.1 j )/0.01

Fnet = 1970 i + 2110 j N

c)

Now ,for the angle beta

beta = arctan(2110/1970)

beta = 47 degree

the angle B is 47 degree

D)

for angle beta to be alpha

the initial velocity of the ball must be zero

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