Question

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

and it reaches a height of 2 + 24t - 4.9t2 after t seconds. How many seconds after the
rock is thrown will it hit the ground? Round your answers to the nearest hundredth.

Answer 1

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=(-24+/-√(24^2-4(-4.9)(2)) )/(2(-4.9)) }` and

`t=(-24+/-√(576+39.2) )/(-9.8)` and

`t=(-24+/-√(615.2) )/(-9.8)` and

the 2 solutions are:

`t=(-24+24.803)/(-9.8)=-.08 sec` and

`t=(-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.