Problem Solution

For this case, let us choose y to be positive up. We than have

     y = g = -9.8 m/s²

     y₀ = 0

     v₀ = +15.0

We can use the equation derived earlier that does not include time (we do not know the time)

     v² = v₀² + 2a(y -y₀)

Since we are interested in finding the max height, y, we solve for y and get

     y = (v² - v₀² - 2ay₀)/2a = (v² - v₀² )/2a  since y₀ = 0

Also, since we know that v is 0 at the max height

     y = v₀² )/2a = 15.0²/(2*-9.8) = 11.5 m