Question

An egg is dropped from the roof of a building. The distance it falls varies directly with the square of the time it falls. If it takes ½ second for the egg to fall eight feet, how long will it take the egg to fall 200 feet?​

Answer 1

Let's first write out the proportionality statement based on the information given:

distance ∝ time^2

We can then write an equation for the relationship between the distance and time:

distance = k(time^2)

where k is the constant of proportionality. We need to solve for k in order to use this equation to answer the question.

We know that when the egg falls for ½ second, it falls 8 feet. Plugging in these values, we get:

8 = k(0.5^2)

8 = 0.25k

k = 32

Now that we have k, we can use the equation to find the time it takes the egg to fall 200 feet. We rearrange the equation to solve for time:

distance = k(time^2)

time^2 = distance/k

time = sqrt(distance/k)

Plugging in the values, we get:

time = sqrt(200/32) = 2.5 seconds

Therefore, it will take the egg 2.5 seconds to fall 200 feet.