We were given the following information:
-65 degree launch angle from the horizontal
-The initial velocity: 92 ft./sec.
-The height of the tower: 160 ft.
For this problem we are solving for the vertex and the x-intercepts:
-Unknown peak of the fireworks
-Unknown distance it will travel
We created a diagram including all the information we were given.
I solved for the vertex. For the middle x point = t I added both x intercepts then divided the sum by 2. I then subtracted 1.44 from the sum because the start of the launch was at (0,0) not (-1.44,0) Then I plugged t which was what we just solved for into the standard formula which gave us h(t). Aka: Peak of fireworks
At first for the vertex, I thought about using the equation h(t)=160+92t-16t^2 and dividing it by 2 and squaring it. But then I ran into a bump and asked why it wasn't working. Then we realized that there was something different about the equation. That it had a number for a=16 instead of just being x an unknown number. So what we had to do instead was get the middle point of 0 to the positive x intercept. Because the launch happens on point 0 not a negative point; this gives us the x intercept. Then we plugged in that sum into the equation for t ; which then gave us the y intecept.