Applying the Quadratic Formula

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.

A) t ≈ 0.87 s

B) t ≈ 4 s

C) t = 8.5 s

D) t = 16 s

Question

Mathematics

Janessa Brown

18 October, 18:29

Applying the Quadratic Formula

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.

A) t ≈ 0.87 s

B) t ≈ 4 s

C) t = 8.5 s

D) t = 16 s

+2

Answers (1)

Know the Answer?

Charlie Mcintyre · Answer 1

B

Step-by-step explanation:

The trick you need to employ is that when the rock hits the ground, the timer stops. So h must be taken as 0.

0 = - 16t^2 + 255 Set up the equation

- 255 = - 16t^2 Divide by - 16

15.9375 = t^2 Switch

t^2 = 15.9375 Take the square root of both sides.

sqrt (t^2) = sqrt (15.9375)

t = 3.992 seconds

The closest answer is B