a rugby ball has a mass of 0.5kg. initially it ... Question A rugby ball has a m

Question

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

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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