While hiking, Marek throws a rock off a cliff that is roughly 10 meters above a lake. This 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 the water, what would be a reasonable scale for the range?(1 point)
Responses
10
10
5
5
2
2
1
Given the equation h = -4.9t^2 + 10, we want to find out when h equals zero, which is when the rock hits the water. To determine a reasonable scale for the range in our table, we need to consider the vertical distance the rock will travel (10 meters, from the cliff to the water) and the motion of the rock due to gravity. Given this, we want a scale that captures the time from the rock being thrown until it hits the water.
Let's solve for t when h = 0:
0 = -4.9t^2 + 10
4.9t^2 = 10
t^2 = 10 / 4.9
t^2 = approximately 2.04
t = sqrt(2.04)
t = approximately 1.43 seconds
The rock will take approximately 1.43 seconds to hit the water. With this in mind, we need a range for time (t) that includes 0 to slightly over 1.43 seconds. We want to have enough increments within this range to accurately show the progress of the rock as it falls.
Given the options provided, a scale of 1 second for t would be reasonable, as it would allow you to capture the motion at every second, including at the starting point (t=0), one second later, and when the rock hits the water slightly after 1 second.
So, a scale of 1 for the range is a reasonable choice, as it allows for a detailed look at the rock's position throughout its fall until it hits the water.