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

Answer:

3.1 seconds

Step-by-step 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 [$t=\frac{-b+-\sqrt{b^2-4ac} }{2a}$ ] to solve this.

a is -16

b is 40 , and

c is 30.

plugging these into the formula we get:

$t=\frac{-b+-\sqrt{b^2-4ac} }{2a}\\t=\frac{-40+-\sqrt{(40)^2-4(-16)(30)} }{2(-16)}\\t=\frac{-40+-\sqrt{3520} }{-32}\\t=-0.6,3.1$

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)