Question

a rock is thrown off a 200-foot cliff. the trajectory of the rock is modeled by the function h(t)=(-10t^2)+200, where h is the height in feet and t is the time in seconds. when will the rock hit the ground.

Answer 1

4.47 seconds.

Explanation:

Given function:

`h(t)=-10t^2+200`

where:

• h is the height (in feet).
• t is the time (in seconds).

The rock will hit the ground when h(t) = 0.

Therefore, set the function to zero and solve for t:

`\begin{aligned}h(t)&=0\\\implies -10t^2+200&=0\\10t^2&=200\\t^2&=20\\t&=\pm√(20)\\t&=-4.47, 4.47\;\; \sf (2\;d.p.)\end{aligned}`

As time is positive, t = 4.47 s only.