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26 March, 03:38

A soccer ball of mass 0.35 kg is rolling with velocity 0, 0, 1.8 m/s, when you kick it. Your kick delivers an impulse of magnitude 1.8 N · s in the - x direction. The net force on the rolling ball, due to the air and the grass, is 0.26 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 vavg ≈ pf /m. (Express your answer in vector form.)

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  1. 26 March, 06:08
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    position 9.58 m

    Explanation:

    In impulse exercises and amount of movement, we always assume that the contact time is small,

    I = Δp

    With this expression we can calculate the final speed

    I = m Vf - m Vo

    Vf = (I + mVo) / m

    Vf = (1.8 + 0.35 1.8) / 0.35

    Vf = 6.94 m / s

    To calculate the acceleration of the ball we use Newton's second law, after finishing the impulse

    ∑ F = m a

    fr = m a

    a = fr / m

    a = - 0.26 / 0.35

    a = - 0.74 m/s²

    A negative sign indicates that this acceleration is slowing the ball

    Now we have speed and time acceleration, so we can use the kinematic equations to find the position at 1.5 s

    X = Vo t + ½ to t²

    In this case Vo is the speed with which the ball comes out after the impulse 6.94

    X = 6.94 1.5 + ½ (-0.74) 1.522

    X = 9.58 m
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