Question

Answer the following questions using what you've learned from this unit. Write your responses in the space provided.

1. (18 points) You are standing at the top of a building that is under construction. Someone drops a box of nails off the side of the building, and you count that it takes at least 5 seconds for the box to hit the ground. The time it takes something to fall from a distance d (in meters) can be found from the equation:

A. Using this equation, figure out the range of possible heights the building has.

B. Later in the day, you decide to try a more precise experiment. You stand at a different height on the building and drop the box of nails, but this time you use a stopwatch. You measure that it took exactly 3.4 seconds for the nails to hit the ground. How high were you when you dropped the nails?

Answer 1

run

Explanation:

Answer 2

1:The range of possible heights for the building is 0 to 4.95 meters.

2: We were 2.87 meters high when we dropped the nails.

Using the equation d = √(2d / 4.9), we can figure out the range of possible heights the building has.

d = √(2d / 4.9)

2d = 4.9d

d = 0

This means that the minimum height of the building is 0 meters.

We can also plug in the value of 5 seconds for the time it takes the box of nails to hit the ground to find the maximum possible height of the building.

d = √(2 * 5 / 4.9)

d = 4.95 meters

This means that the maximum possible height of the building is 4.95 meters.

Therefore, the range of possible heights for the building is 0 to 4.95 meters.

2:B. If we measure that it took exactly 3.4 seconds for the nails to hit the ground, we can use the same equation to find how high we were when we dropped the nails

d = √(2 * 3.4 / 4.9)

d = 2.87 meters

Therefore, we were 2.87 meters high when we dropped the nails.