Question

the height h in feet of a projectile launched vertically upward from the top of a 96-foot tall tower when time is given by . how long will it take the projectile to strike the ground? what is the maximum height that the projectile reaches?

Answer 1

4 ac - b²/4a

= 4 (-16)(110) - (16)²/ 4(-16) = 114

- b /2a = -(16)/2(-16) = 1/2 is the time it will take to reach the max height.

let t = 3 => h(t) = 110 + 16(3) - 16(3)² => 14

let t = 4 => h(t) = 110 + 16(4) - 16(4)² => -82

So the projectile will strike the ground around 3 and 4 seconds and the reason behind is that the positive h(t) leads to being above the ground and the negative h(t) value will indicate that the object is  below the ground which is not possible in any way.