A soccer ball of mass 0.50 kg is rolling with velocity m/s when you kick it. Your kick delivers an impulse of magnitude 1.5 N · s in the - x direction. The net force on the rolling ball, due to the air and the grass, is 0.29 N in the direction opposite to the direction of the ball's momentum. Using a time step of 0.5 s, find the position of the ball at a time 1.5 s after you kick it, assuming that the ball is at the origin at the moment it is kicked. Use the approximation

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Mathematics

Nico Berg

29 September, 14:40

A soccer ball of mass 0.50 kg is rolling with velocity m/s when you kick it. Your kick delivers an impulse of magnitude 1.5 N · s in the - x direction. The net force on the rolling ball, due to the air and the grass, is 0.29 N in the direction opposite to the direction of the ball's momentum. Using a time step of 0.5 s, find the position of the ball at a time 1.5 s after you kick it, assuming that the ball is at the origin at the moment it is kicked. Use the approximation

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Nathanial Rasmussen · Answer 1

We are given with the impulse which will allow us to determine the velocity of the ball after the kick

1.5 = 0.5 (v - 1.8)

v = 4.8 m/s

We can determine the acceleration using newton's second law of motion

0.29 = 0.5 a

a = 0.58 m/s2

Using the formula for kinematics

y = v0t + 0.5at^2

y = 4.8 (1.5) + 0.5 (0.58) (1.5) ^2

y = 7.85 m to the left of the origin