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21 December, 19:33

A superhero swings a magic hammer over her head in a horizontal plane. The end of the hammer moves around a circular path of radius 1.50 m at an angular speed of 6.00 rad/s. As the superhero swings the hammer, she then ascends vertically at a constant 2.00 m/s. What is the speed of the end of the hammer relative to the ground?

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  1. 21 December, 21:27
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    Answer: 9.22 m/s

    Explanation:

    Given

    Radius of circular path, r = 1.5 m

    Angular speed of hammer, w = 6 rad/s

    Vertical component of speed, v (v) = 2 m/s

    First, the horizontal component of speed is given by

    v (h) = wr

    v (h) = 1.5 * 6

    v (h) = 9 m/s

    Now, the speed of the hammer relative to the ground would be gotten if we find the resultant between both the horizontal and vertical component

    v = √[v (h) ² + v (v) ²]

    v = √ (9² + 2²)

    v = √ (81 + 4)

    v = √85

    v = 9.22 m/s
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