a hailstone falls from a cloud at a height of 1,600 ft. if the equation for height as a function of time is…

a hailstone falls from a cloud at a height of 1,600 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 hailstone to hit the ground? ? seconds

a hailstone falls from a cloud at a height of 1,600 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 hailstone to hit the ground? ? seconds

Answer

Explanation:

Step1: Set up the equation

When the hailstone hits the ground, $h(t)=0$. The initial - height is 1600 ft, so the equation is $0=-16t^{2}+1600$.

Step2: Rearrange the equation

Add $16t^{2}$ to both sides of the equation: $16t^{2}=1600$.

Step3: Solve for $t^{2}$

Divide both sides of the equation by 16: $t^{2}=\frac{1600}{16}=100$.

Step4: Solve for $t$

Take the square - root of both sides. Since $t$ represents time, we consider the positive square root. $t = \sqrt{100}=10$.

Answer:

10