At time seconds, the mass has angular speed
and hence linear speed
After 8 s, its linear speed is
and has centripetal acceleration with magnitude
To maintain this linear speed, by Newton's second law the required centripetal force should have magnitude
Explanation:
Given that,
Initial speed of the rock, u = 30 m/s
The acceleration due to gravity at the surface of the moon is 1.62 m/s².
We need to find the time when the rock is ascending at a height of 180 m.
The rock is projected from the surface of the moon. The equation of motion in this case is given by :
It is a quadratic equation, after solving whose solution is given by:
t = 7.53 s
or
t = 8 seconds
(e)If it is decending, v = -20 m/s
Now t' is the time of descending. So,
Let h' is the height of the rock at this time. So,
or
h' = 155 m