Question

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 1

Answer:

10 seconds

Step-by-step explanation:

The function is

$h(t)=-16t^2+\text{Initial height}$

Initial height = 1600 ft

t = Time taken

$0=-16t^2+1600$

$\Rightarrow -16t^2=-1600$

$\Rightarrow t^2=\dfrac{1600}{16}$

$\Rightarrow t^2=100\\\Rightarrow t=\pm 10$

So, time taken by the hailstone to reach the ground is $10\ \text{seconds}$.