When you drop a penny off the roof of a building, it takes 16 seconds to reach the ground. How high is the roof?

Explanation:

I'll do this in both meters and feet, since you don't specify which you need. Since we are only dealing in the y-dimension:

Δx = ???

a = -9.8 m/s/s

v₀ = 0

t = 16 sec

In the equation:

Δx = v₀t + we fill in accordingly:

Δx = which simplifies to

Δx = so

Δx = -1300 m. Now in feet, it's the same equation but the acceleration is -32 ft/s/s:

Δx = which is

Δx = -4100 ft (the negative signs here just indicate direction: the penny is this distance below the point from which it was dropped. So, obviously, to answer the question regarding the height of the building, you would say it was 1300 m high or 4100 feet high. The negative would be significant if we were asked instead "How far did the penny fall?" which would be the same answer to a slightly different question.)

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