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6 September, 02:00

During a tennis serve, a racket is given an angular acceleration of magnitude 155 rad/s2. At the top of the serve, the racket has an angular speed of 20.0 rad/s. If the distance between the top of the racket and the shoulder is 1.40 m, find the magnitude of the total acceleration of the top of the racket.

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  1. 6 September, 05:56
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    600.6 m/s^2

    Explanation:

    α = 155 rad/s^2

    ω = 20 rad/s

    r = 1.4 m

    Tangential acceleration, aT = r x α = 1.4 x 155 = 217 m/s^2

    Centripetal acceleration, ac = rω^2 = 1.4 x 20 x 20 = 560 m/s^2

    The tangential acceleration and the centripetal acceleration both are perpendicular to each other. Let a be the resultant acceleration.

    a^2 = aT^2 + ac^2

    a^2 = 217^2 + 560^2

    a = 600.6 m/s^2
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