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nydimaria [60]
3 years ago
7

A trebuchet launches a projectile from a hilltop 30 feet above ground level on a parabolic arc at a velocity of 40 feet per seco

nd. 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)
Mathematics
1 answer:
Gennadij [26K]3 years ago
7 0

Answer:

3.1 seconds

Step-by-step explanation:

The time it will hit the ground is when the <em>height is equal to 0</em>. 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)

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