Aball is thrown straight up from the edge of a 15 foot balcony with initial velocity 40 feet/sec. how high will the ball travel?

Hello
The initial height of the ball is , while the initial velocity is .
This is a uniformly accelerated motion, where the acceleration is the gravitational acceleration: , where the negative sign means that the acceleration points downwards. 
We can proceed in two steps: 

1) First of all, we calculate the time the ball needs to reach the maximum height. At the point of maximum height, the velocity is zero: . 
We can use the formula

To find the time:


2) At this point, we can calculate the total height reached by the ball after this time, i.e. the maximum height: