Question

5. A rock is thrown vertically from the ground with a velocity of 24 meters per second,

Answer 1

Answer:

Step-by-step explanation:

$h(t)=-4.9t^2+24t+2$ is our quadratic,where h(t) is the height of the object after t seconds. If we are looking for how long, t, it takes the object to hit the ground, h(t) will be equal to 0 since the height of something on the ground is 0. We set the quadratic equal to zero and factor it using the quadratic formula:

$t=\frac{-24+/-\sqrt{24^2-4(-4.9)(2)} }{2(-4.9)} }$ and

$t=\frac{-24+/-\sqrt{576+39.2} }{-9.8}$ and

$t=\frac{-24+/-\sqrt{615.2} }{-9.8}$ and

the 2 solutions are:

$t=\frac{-24+24.803}{-9.8}=-.08 sec$ and

$t=\frac{-24-24.803}{-9.8}=4.98sec$

and since time can never be negative, we know that it takes 4.98 seconds for the rock to hit the ground under the given conditions.