A small space telescope at the end of a tether line of length L moves at linear speed v about a central space station. What will be the linear speed of the telescope if the length of the line is changed to x*L ? x = 2.8; v = 2 m/s?

The answer to the question is

The linear speed of the telescope will be 5.6 m/s if the length of the line is changed to x*L where  x = 2.8; and initial velocity v = 2 m/s

Explanation:

Speed = v₁ = ωL = 2 m/s

When the line is changed to x*L where x = 2.8 the linear speed will be

v₂ = 2.8 × L× ω = 2.8× 2 = 5.6 m/s

The linear speed varies with the angular speed following the relation v/r =ω where

ω = angular speed

v = linear speed and

r = radius of the path of travel of the object at the vertex