Question

A small toy rocket is launched from a 24-foot pad. The height (h, in feet) of the rocket t seconds after

taking off is given by the formula
h = - 2t^2+ 2t + 24.
How long will it take the rocket to hit the
ground?

Answer 1

4 seconds

Explanation:

Since we want to know the time when the height is 0, we can rewrite the problem as
`0=-2t^2+2t+24`. From there, we can plug it into the quadratic formula, which gives us
`(-2-√(4-4(-2)(24)) )/(2(-2))`(Since it's a real-world problem and we have a negative denominator, we won't be using the positive square root). We simplify this to get
`(-2-√(196) )/(-4)`, then
`(-2-14)/(-4)`. Finally, we can calculate this to be 4 seconds.