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.

Question

Physics

Maximus Salazar

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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Answers (1)

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Jared Mason · Answer 1

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