Question

The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equation h = -16t2 + h0, where h0 is the initial height of the object. Suppose a small rock dislodges from a ledge that is 255 ft above a canyon floor. Solve the equation h = -16t2 + 255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor.

Answer 1

Ok all we have to do is substitute in the values. We get from the enunciate that the initial height of the small rock is at 255 ft, and it is asking the time it takes to get to the canyon floor (which means final height equals 0).

h = -16t2 + h0 , we substitute values in

0 = -16t2 + 255, we solve for t2

-t2 = -255/16 ; -t2=-15.93, we then multiply both sides of the equation by -1

t2 = 15.93, sq root both sides of the equation

t = 3.99 , which probably is t=4 because I didn't use all decimals in the calculations.

Answer 2

t = 4

Explanation:

We have been given,
`h=-16t^(2)+255`

The initial height of the small rock is at 255 feet and the final height is at 0 feet.

So, equation becomes: (putting h = 0)

`0=-16t^(2)+255`

=>
`16t^(2) =255`

=>
`t^(2)=15.937`

=>
`t=√(15.937)`

t = 3.9921 approximately t = 4 seconds.