Question

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

t=4

Explanation:

ed2020

Answer 2

The time it takes the rock to reach the canyon floor is approximately 4 seconds.

Explanation:

The equation representing the height h (in feet) of an object t seconds after it is dropped is:

`h=-16t^(2)+h_(0)`

Here, h₀ is the initial height of the object.

It is provided that a small rock dislodges from a ledge that is 255 ft above a canyon floor.

That is, h₀ = 255 ft.

So, when the rock to reaches the canyon floor the final height will be, h = 0.

Compute the time it takes the rock to reach the canyon floor as follows:

`h=-16t^(2)+h_(0)`

`0=-16t^(2)+255\\\\16t^(2)=255\\\\t^(2)=(255)/(16)\\\\t^(2)=15.9375\\\\t=√(15.9375)\\\\t=3.99218\\\\t\approx 4`

Thus, the time it takes the rock to reach the canyon floor is approximately 4 seconds.