# Math Help - Quadratic functions (projectile motion) question

1. ## Quadratic functions (projectile motion) question

So I have this problem that I am unsure of how to solve. We did it in class earlier this year but I am unsure of what to do.

Question:

Bob throws a ball in the air at 55 feet per second at an angle of 30(degrees), from an initial height of 10 feet. At the same time, Sue throws a different ball at 50 feet per second from an initial height of 5 feet, and at an angle of 60(degrees). Find the time when each ball hits the ground. Find the max height of each ball. Find the length of time that each ball is higher than 20 feet off the ground. Find the time(s) that the two balls are at the exact same height. What would have to be true for the two balls to collide at one of those moments.

I know the formula is h(t)= -16t(squared) + ( v sin A)t + h

Which would be h(t)= -16t(squared) + (55sin30)t + 10

But I am unsure of how to find the answers.

2. ## Re: Quadratic functions question

To find what time the balls hit the gorund make h(t)=0

For a quadratic equation of the form $0= at^2+bt+c \implies t = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

What do you get?

3. ## Re: Quadratic functions question

2.03 seconds is what I got for the first ball at hitting the ground.

How am I to find the max height? Length in time that each ball is higher than 20 ft off the ground?

4. ## Re: Quadratic functions question

The max height can be found halfway between the 2 zeros.