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Bingel
3 months ago
11

A superhero swings a magic hammer over her head in a horizontal plane. The end of the hammer moves around a circular path of rad

ius 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? What is the magnitude of acceleration of the end of the hammer? What is the direction of acceleration of the end of the hammer measured as an angle between a⃗and the direction toward the center of the circular path?
Physics
1 answer:
Keith_Richards [3.2K]3 months ago
3 0

Answer:

9.21954 m/s

54 m/s²

The angle is zero

Explanation:

r = Length of the arm = 1.5 m

\omega = Angular velocity = 6 rad/s

The speed's horizontal component can be calculated using

v_h=\omega r\\\Rightarrow v_h=6\times 1.5\\\Rightarrow v_h=9\ m/s

The vertical speed is determined by

v_v=2\ m/s

The combination of these two components yields the hammer’s speed in relation to the ground

v=\sqrt{v_h^2+v_v^2}\\\Rightarrow v=\sqrt{9^2+2^2}\\\Rightarrow v=9.21954\ m/s

The hammer’s speed relative to the ground measures 9.21954 m/s

Acceleration in the vertical direction is zero

The total acceleration is expressed as

a_n=a_h=\omega^2r\\\Rightarrow a_n=6^2\times 1.5\\\Rightarrow a_n=54\ m/s^2

Total acceleration is 54 m/s²

Since acceleration points towards the center, the angle remains zero.

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