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?

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