Help Me Calculate How high SuperMan can Jump!

1. The problem statement, all variables and given/known data
This is a semester review. I am having trouble starting the second part of this question. It is well-know fact that Superman is "faster than a speeding bullet, more powerful than a locomotive, and able to leap tall buildings in a single bound." Assume his mass is 100kg.

The first part we are given his initial velocity as 181 m/s. That is one meter faster than a characteristic bullet. His jump takes off at a 86.9 degree angle. What are his initial velocities in the x and y direction. No trouble here.

V(xinitial)=1.26 m/s
V(yinitial)=180.99 m/s

The second part asks how tall of a building can he leap using the above data.

2. Relevant equations



3. The attempt at a solution
I have his initial velocities in the x and y direction. I am confused on how to solve for a final velocity without knowing time or the final velocity in the y direction. I am thinking that since I have two unknowns I might have to rearrange and equation and substitute it into another one to solve for one unknown. Any help is greatly appreciated!
Here's a hint: when superman is at the highest point in his jump, his vertical velocity (let's call this his "y velocity") is zero. (He starts with a positive y velocity, and if his y velocity were positive at the peak of his jump, he'd keep going up--so it wouldn't be the peak of his jump). So you can use V_y=0 for your final velocity. The horizontal or x velocity doesn't really matter in this problem, since it stays constant throughout. Honestly, including a small x velocity in this problem is probably just meant to confuse you.

However, I think there's an easier way to solve this problem. Use kinetic and potential energies.
Thanks for the hint. I had missed that key information. I have to solve this using projectile motion and not energy so thanks anyway. I'll post questions if I have anymore.


Homework Helper
When the super man reaches the highest point of the building, his Vy(final) can be taken as zero.

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