Question

A trebuchet launches a projectile from a hilltop 30 feet above ground level on a parabolic arc at a velocity of 40 feet per second. The equation h = −16t2 + 40t + 30 models the projectile's h height at t seconds. How long will it take for the projectile to hit its target on the ground? (to the nearest tenth of a second)

Answer 1

3.1sec

Explanation:

Answer 2

3.1 seconds

Explanation:

The time it will hit the ground is when the height is equal to 0. So we plug in 0 in h and solve the quadratic equation for t.

`-16t^2+40t+30=0`

We will use the quadratic formula [
`t=(-b+-√(b^2-4ac) )/(2a)` ] to solve this.

a is -16

b is 40 , and

c is 30.

plugging these into the formula we get:

`t=(-b+-√(b^2-4ac) )/(2a)\\t=(-40+-√((40)^2-4(-16)(30)) )/(2(-16))\\t=(-40+-√(3520) )/(-32)\\t=-0.6,3.1`

Since time cannot be negative, we take t = 3.1 as the value

So it will take 3.1 seconds to hit the ground (target)