Question

a bird releases waste from a height of 400 feet. if the equation for height as a function of time is h(t) = -16t² + initial height where t is time in seconds and h(t) is height in feet, how many seconds will it take for the waste to hit the ground? ? seconds

Explanation:

Step1: Set up the equation

When the waste hits the ground, $h(t)=0$. The initial height is 400 feet, so the equation becomes $0=-16t^{2}+400$.

Step2: Rearrange the equation

Add $16t^{2}$ to both sides: $16t^{2}=400$.

Step3: Solve for $t^{2}$

Divide both sides by 16: $t^{2}=\frac{400}{16}=25$.

Step4: Solve for $t$

Take the square - root of both sides. Since $t$ represents time and cannot be negative in this context, $t = \sqrt{25}=5$.

Answer:

5