Atetherball is attached to a pole with a 2.0-m rope. it is circling at 0.20 rev/s. as the rope wraps around the pole it shortens. how long is the rope when the ball is moving at 5.0 m/s?

The length of the rope  is 1.005 m.

Explanation:

Given that,

Length of rope = 2.0 m

Angular speed = 0.20 rev/s

Linear speed = 5.0 m/s

Since there are no external torques about the rotation  axis

We need to calculate the length of the rope

Using conservation of angular momentum

Put the value into the formula

Hence, The length of the rope  is 1.005 m.

resonant frequency

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west