Pendulum question in physics 11 2D forces

Question

A student swings on a long rope of length L=5m. The student starts by pulling back at an angle of 𝜃𝜃 = 30º as shown below.

a. Determine the initial height of the student by solving the highlighted right triangle shown below. (hint: the length of the rope is ALWAYS 5m, i.e. y+h = 5m)

b. Use your answer from (a) combined with conservation of energy to determine the speed at the bottom.

https://www.wired.com/wp-content/uploads/2015/01/sketches_fall_14_key6.jpg, diagram for the question, length is 5m and theta is 30.

Answer 1

First find the height that the student is above ground by determining the y as shown in my diagram where the y length is equal to 5 m times the cosine(30). Since the length of the pendulum is 5 m the height h is equal to 5-5 cos(30) which came out to be 1.67 meters. Since we have potential energy at the top of the swing which turns into kinetic energy at the bottom we can set the potential energy which is equal to mgh equal to the kinetic energy at the bottom which is equal to one half mv squared. Notice that the mass cancels, so we have the velocity squared equals to 2 times gravity times the h. The velocity came out to be 5.72 m/s