Question

cc.2.2.hs.c.6
a rock falls from a height of 80 feet. the equation that
gives the height of the rock (in feet) above the ground as a
function of time (in seconds) is

h(t) = -16t² + 80

how many seconds will it take for the rock to hit the
ground?

○ 4.5 seconds

○ 1.4 seconds

○ 2.2 seconds

○ 3.9 seconds

Explanation:

Step1: Set height to 0

When the rock hits the ground, \( h(t) = 0 \). So we set up the equation \( 0 = -16t^2 + 80 \).

Step2: Solve for \( t^2 \)

First, subtract 80 from both sides: \( -80 = -16t^2 \). Then divide both sides by -16: \( t^2=\frac{80}{16}=5 \).

Step3: Solve for \( t \)

Take the square root of both sides: \( t = \sqrt{5}\approx2.2 \) (we take the positive root since time can't be negative).

Answer:

C. 2.2 seconds