A bird drops a stick to the ground from a height of 60 ft. The function h=-16t^2+60 gives the stick's approximate height h above the ground, in feet, after t seconds. At about what time does the stick hit the ground?

Question

A bird drops a stick to the ground from a height of 60 ft. The function h=-16t^2+60  gives the stick's approximate height h above the ground, in feet, after t seconds. At about what time does the stick hit the ground?
The stick hits the ground at about

GPT 3.5 · Answer

To find out when the stick hits the ground, we need to find the value of t when the height h is equal to 0.

We have the equation h = -16t^2 + 60.

Setting h = 0, we get:
0 = -16t^2 + 60.

We can rearrange this equation by subtracting 60 from both sides:
-60 = -16t^2.

Now divide both sides by -16 to isolate t^2:
t^2 = 60/16.

Simplifying further:
t^2 = 15/4.

To find the value of t, we take the square root of both sides:
t = ± √(15/4).

The stick cannot have a negative time, so we take the positive square root:
t = √(15/4).

The square root of 15 divided by 2 is approximately 1.94.

Therefore, the stick hits the ground at about 1.94 seconds.