Question

HELP

Answer 1

Answer:

The time it takes for the cannonball to hit the ground is 6.49 seconds.

Step-by-step explanation:

You know that the height of the cannonball above the ground, h, in meters, in time, t, in seconds, is found by the function h(t) = -4.9t² + 30.5t + 8.4. You want to calculate the time it takes for the cannonball to hit the ground, that is, the time it takes for the bullet to reach zero height. So, being h(t) = 0 you have:

0 = -4.9t² + 30.5t + 8.4

To solve a quadratic function 0=a*x² + b*x +c, the expression is applied:

$\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a}$

In this case, being a = -4.9, b =30.5 and c =8.4  you have:

$\frac{-30.5+-\sqrt{30.5^{2} -4*(-4.9)*8.4} }{2*(-4.9)}$

Solving you get:

t1= -0.26 seconds and t2=6.49 seconds

Since time does not have a negative value, then the time it takes for the cannonball to hit the ground is 6.49 seconds.