Solve the problem.
-The distance that an object falls when it is dropped is directly proportional to the square of the amount of time since it was dropped. An object falls 39.2 meters in 2 seconds. Find the distance the object falls in 5 seconds.
A) 10 m
B) 98 m
C) 245 m
D) 49 m

Question

Quizplus · Accepted Answer

Let D be the distance the object falls in 5 seconds. Then,

D/39.2 = (5^2)/(2^2)

D/39.2 = 25/4

D = (39.2*25)/4

D = 245 meters.

Therefore, the correct answer is (C). We can set up a proportion using the information given:

(distance)/(time^2) = k  (where k is the constant of proportionality)

Using the first data point, we can substitute in and solve for k:

39.2/2^2 = k
k = 9.8

Now we can use this value of k to find the distance for the second data point:

(distance)/(5^2) = 9.8

distance = 245 meters.

Therefore, the answer is choice C.

Solve the Problem. -The Distance That an Object Falls When It Is Dropped