Answer:
Explanation:
Good job on creating a testable equation.
Maybe you need to know what to do with it.
If we can find a real solution or two, then the projectile will reach the 100 ft altitude. (I'm fairly certain it will given that high initial velocity)
If we cannot find a real solution, then the rocket will fail to reach the altitude goal.
-16t² + 80t + 4 = 100
we will want a zero on the right hand side, so subtract 100
-16t² + 80t - 96 = 0
we can simplify even further by dividing everything by -16
t² - 5t + 6 = 0
which can be factored
(t - 3)(t - 2) = 0
so either
t = 3 s
or
t = 2 s
So the projectile reaches the 100 ft level twice,
at two seconds after launch while rising and
at three seconds after launch while falling.
Lets see what happens when we set the goal a bit higher, say 108 ft
-16t² + 80t + 4 = 108
-16t² + 80t - 104= 0
-2t² + 10t - 13 = 0
not easily factored so let's use quadratic formula
t = (-10 ±√(10² - 4(-2)(-13))) / (2(-2)
t = (-10 ±√-4) / -4
As √-4 = 2i is an imaginary number, there are no real solutions and the projectile will not reach 108 ft.