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

h=-16t^2+255
-255=-16t^2
15.9375=t^2
3.99=t

Answer 2

The rock will reach to the canyon floor in 3.99 seconds.

Explanation:

The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equation

`h=-16t^2+255`

Where, h0 is the initial height of the object.

It can be written as

`h=-16t^2+0t+255`

The height of the object is zero if it will reach to the canyon floor.

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

Quadratic formula:

`t=(-b\pm √(b^2-4ac))/(2a)`

Here a=-16, b=0 and c=255.

`t=(-0\pm √(0^2-4(-16)(255)))/(2(-16))`

`t=(\pm √(16320))/(-32)`

`t=\pm 3.99`

Time cannot be negative, therefore the rock will reach to the canyon floor in 3.99 seconds.