A child slides without friction from a height h along a curved water slide. She is launched from a height h/5 into the pool. Determine her maximum airborne height Y_max in terms of h and the launch angle theta.

Pools and slides! a beautiful and healthy fun. Ideal for summer afternoons. Today we will study a combined exercise joined mechanical energy balance with launching projectiles.
What are we asking? the maximum airborne height... What will we need? launch speed ... How will we get? with mechanical energy balance ...
We will begin by calculating the launch velocity making a energy balance between the starting point (the highest part of the slide that we call point A) and launch point (the lower part of the slide that we call point B). At point A all energy is potential. At point B a part of that energy is transformed into kinetic energy and another part remains in the form of potential energy. Let's see what has been said in equations:

Now that we have the launch speed only need use an equation of launch projectiles to find the expression of the maximum airborne height as a function of the launch speed:

we have solved the problem as we can see the result is a function of the height and launch angle as we had asked in the problem statement. Every time you see a physics problem that looks complicated remember all the problems that are difficult are the union of several easy problems. We solved two problems here one was find the launch velocity with the energy balance and the second was find the maximum airborne height with a given launch speed.
This was all in this post. if you like our work share it with your friends! see you later! and remember ... physics it's easy! very easy... ;)