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27 March, 05:10

Two soccer players, Mia and Alice, are running as Alice passes the ball to Mia. Mia is running due north with a speed of 6.00 m/s. The velocity of the ball relative to Mia is 5.00 m/s in a direction 30.0 east of south. What are the magnitude and direction of the velocity of the ball relative to the ground?

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  1. 27 March, 06:33
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    v_b = 10.628 m / s (13.605 degrees east of south)

    Explanation:

    Given:

    - Velocity of mia v_m = + 6 j m/s

    - Velocity of ball wrt mia v_bm = 5.0 m/s 30 degree due east of south

    Find:

    What are the magnitude and direction of the velocity of the ball relative to the ground? v_b

    Solution:

    - The relation of velocity in two different frame is given:

    v_b - v_m = v_bm

    - Components along the direction of v_b, m:

    v_b*cos (Q) - v_m*cos (30) = 5

    v_b*cos (Q) = 5 + 6 sqrt (3) / 2

    v_b*cos (Q) = 5 + 3sqrt (3)

    - Components orthogonal the direction of v_b, m:

    -v_m*sin (30) = v_b*sin (Q)

    -6*0.5 = v_b*sin (Q)

    -3 = v_b*sin (Q)

    - Divide two equations:

    tan (Q) = - 3 / 5 + 3sqrt (3)

    Q = arctan ( - 3 / 5 + 3sqrt (3)

    Q = - 16.395 degrees

    v_b = - 3 / sin (-16.395)

    v_b = 10.63 m/s
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