A simple pendulum consists of a small ball attached to the end of a string of length
2.00 m. The pendulum is displaced to an angle of 60.0 degrees from the vertical as
shown below and given an initial speed of 4.00 m/s. What is the speed of the ball (in
m/s) when it passes through the lowest point in its path?

Question

A simple pendulum consists of a small ball attached to the end of a string of length 
2.00 m. The pendulum is displaced to an angle of 60.0 degrees from the vertical as 
shown below and given an initial speed of 4.00 m/s. What is the speed of the ball (in 
m/s) when it passes through the lowest point in its path?

anonymous · Answer

use conservation of energy

$$mgh _{1}+1/2mv _{1}^{2}= mgh _{2}+ 1/2mv _{2}^{2}$$
taking the equlibrium position as the ground level

$$gh +1/2v _{1}^{2}= 1/2v _{2}^{2}$$
find h with the help of the given angle, and length of string
(v1= velocity given; v2= velocity we want to find)