a package is dropped from a helicopter from a height of 3,136 ft. if the equation for height as a function…

a package is dropped from a helicopter from a height of 3,136 ft. 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 package to hit the ground?

a package is dropped from a helicopter from a height of 3,136 ft. 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 package to hit the ground?

Answer

Explanation:

Step1: Set height to 0

When the package hits the ground, $h(t)=0$. The initial height is 3136 ft, so the equation becomes $0=-16t^{2}+3136$.

Step2: Rearrange the equation

Add $16t^{2}$ to both sides: $16t^{2}=3136$.

Step3: Solve for $t^{2}$

Divide both sides by 16: $t^{2}=\frac{3136}{16}=196$.

Step4: Solve for $t$

Take the square - root of both sides. Since $t$ represents time and cannot be negative, $t = \sqrt{196}=14$.

Answer:

14