# Potential energy of string and rock

hi, im new here..can you please help me understand this problem below? actually i have the solution already but i don't get it..sorry im so stupid..

here's the problem:
A small rock with mass .12 kg is fastened to a massless string with length .8 m to form a pendulum. The pendulum is swinging so as to make a maximum angle of 45 degrees with the vertical. Air resistance is negligible. a) What is the speed of the rock when the string passes through the vertical position? b) What is the tension in the string when it makes an angle of 45 degrees with the vertical? c) What is the tension in the string as it passes through the vertical?

the solution is in the attached file...

the problem is i don't know how the "y" in the U = mgy became l( 1- cos theta). that's the only thing i don't understand. im really poor when it comes to problems involving angles. please bear with me...

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The y is simply the elevation from the lowest point of the rock (mass) when it swings in the circular trajectory. In the vertical position, the rock is at a distance l from the pivot (other end of the massless string). As the string and rock rotate (angle $\theta$) from the vertical, the elevation increases l - projection of l to the vertical.
Let l be the hypotenuse of a triangle, then determine the projection (length) onto the vertical based on the angle $\theta$ between l and the vertical.