Question

If a certain cannon is fired from a height of 9.4 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)=-4.9t^2+30.5t+9.4. Find the time it takes for the cannonball to strike the ground.

Answer 1

Answer:

6.5 s

Step-by-step explanation:

The equation provided provides us with the height of the canonball at any time t. When the ball hits the ground, the height of the ball above the ground is zero.

Therefore

h(t)=-4.9t^2+30.5t+9.4 = 0

We then solve for t. Seeing as this is a quadratic equation, we can use the quadratic formula:

$t = \frac{-30.5-\sqrt{30.5^{2} -4(-4.9)(9.4)} }{2(-4.9)} = 6.5 s$

The quadratic formula gives two answers, a positive one and a negative one. The positive one is after time zero and the negative one is before time zero. We are interested in the one after time zero (time zero being the time when the canon is fired)