Question

while taking a photograph on a balcony, you drop your cell phone. the function $y = -16t^2 + 324$ represents the height $y$ (in feet) of the phone $t$ seconds after it is dropped. after how many seconds does the phone land on the ground? time: $\square$ seconds

Explanation:

Step1: Set height to 0

When the phone lands on the ground, the height \( y = 0 \). So we set up the equation \( 0=-16t^{2}+324 \).

Step2: Solve for \( t^{2} \)

First, we can rearrange the equation to isolate \( t^{2} \). Add \( 16t^{2} \) to both sides of the equation: \( 16t^{2}=324 \). Then divide both sides by 16: \( t^{2}=\frac{324}{16}=\frac{81}{4} \).

Step3: Solve for \( t \)

Take the square root of both sides. Since time cannot be negative in this context, we only consider the positive square root. \( t = \sqrt{\frac{81}{4}}=\frac{9}{2} = 4.5 \).

Answer:

\( 4.5 \)