While hiking, Marek throws a rock off a cliff that is roughly 10 meters above a lake. The situation is modeled by the equation: h = -4.9t² + 10, with h representing the height in meters, and t the time in seconds. If you were to set up a table to determine when the rock hits he water, what would be a reasonable scale for the range?

Question

A. 5
B. 2
C. 10
D. 1/10

Answer 1

To determine when the rock hits the water, we need to find the time $t$ when the height $h$ is 0. The equation given is:

$$h=-4.9t^2+10$$

Setting $h$ equal to 0 to find the time when the rock hits the water, we have:

$$0=-4.9t^2+10$$

Rearranging this gives:

$$4.9t^2=10$$

Now, dividing both sides by 4.9:

$$t^2=\frac{10}{4.9}$$

Calculating $\frac{10}{4.9}$:

$$t^2\approx 2.04$$

Taking the square root:

$$t\approx \sqrt{2.04}\approx 1.43\text{ seconds}$$

Now that we established the time when the rock hits the water is around 1.43 seconds, we can set up a table to model the time variable $t$.

A reasonable scale for the range of time can be chosen based on how often we want to record the height values leading up to the time of impact. The options provided are:

A. 5 seconds
B. 2 seconds
C. 10 seconds
D. 1/10 seconds

Given that we are only interested in the time leading up to about 1.5 seconds, a scale of 1/10 seconds (D) would provide a sufficiently detailed view of the height at shorter intervals as the rock falls. This will show how the height decreases over time more granularly than the other options.

Thus, the best answer is D. 1/10 seconds.