Question

If a certain cannon is fired from a height of 8.7 meters above the ground, at a certain angle, the height of the cannonball

above the ground, h, in meters, at time, t, in seconds, is found by the function h(t)=-4.9t² + 30.5t+8.7. Find the time it
takes for the cannonball to strike the ground.

Answer 1

6.50 seconds

Explanation:

You want the time it takes for a cannonball to hit the ground if it has a height function of h(t) = -4.9t² +30.5t +8.7.

Ground

We presume the height is zero when the cannonball hits the ground. That means you want the positive value of t that satisfies ...

0 = -4.9t² +30.5t +8.7

We can use the quadratic formula with a=-4.9, b=30.5, c=8.7 to find the value of t:

`t=(-b\pm√(b^2-4ac))/(2a)=(-30.5\pm√(30.5^2-4(-4.9)(8.7)))/(2(-4.9))\\\\=(30.5+√(1100.77))/(9.8)\approx6.4977`

It takes about 6.50 seconds for the cannonball to strike the ground.