Question

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1. A rock is dropped from a height of 100 feet. Calculate the time between when the rock was dropped and when it landed. If we choose "down" as positive and ignore air friction, the function is
h(t)=25²-81.
O t=3.24 seconds
O t=9 seconds
O t=1.8 seconds
O t=6.48 seconds

Answer 1

Answer: t = 1.8 seconds

Explanation:

The function h(t) = 25t^2 - 81 gives the height of the rock (in feet) at time t seconds after it was dropped.

When the rock lands, its height is 0. So we can set h(t) = 0 and solve for t:

25t^2 - 81 = 0

Solving for t, we get:

t = ±√(81/25) = ±(9/5)

Since we are only interested in the time after the rock was dropped, we take the positive value:

t = 9/5 = 1.8 seconds

Therefore, the time between when the rock was dropped and when it landed is 1.8 seconds.

So the answer is: t = 1.8 seconds