Needed help solving this math problem.

Question

The height and feet of an airborne tee shirt t seconds after being launched can be approximated by height = -15t^2 + 135t + 10, 0 < t <

Help me find the times where the tee shirt will reach the fan at 220 feet above ground level in seconds please. 

Answer 1

So, the first thing I usually do is look at what I know and what I want to find out. So, I know the equation for the path the tee shirt will take after being launched. The problem also gives a specific height. So, the only thing I don't know is the times the tee shirt will reach the height of 220 feet. Next, I think about what equation I should use. This isn't too difficult, since they already gave you the equation for height:

H= -15t²+135t+10

With the given height, this becomes

220= -15t²+135t+10

In order to solve for t, I want to set the equation to zero. This can be done by subtracting 220 from both sides:

0= -15t²+135t-210

Since the equation is quadratic, we can use the quadratic formula to solve for the time:

t= [ -b +/- square root (b²-4ac) ] / 2a

where a, b, and c are the first, second, and third coefficients (a=-15, b=135, c=-210).

t= 2, 7 seconds. This means that the tee shirt will reach 220 feet first when it is rising, then again when it is falling back down.

Hope this helps! Let me know if you are still having trouble.