Solve the problem by writing a variation model. An object in free fall travels a distance s that is directly proportional to the square of the time t . If an object falls 960 feet in 8 seconds, how far will it fall in 10 seconds?
A) 1,260 ft
B) 1,320 ft
C) 1,440 ft
D) 1,380 ft
E) 1,500 ft

Question

Quizplus · Accepted Answer

Let k be the constant of proportionality. Then we have:
s = kt^2
We are given that s = 960 when t = 8. Therefore:
960 = k(8^2)
k = 15
So the model for s is:
s = 15t^2
To find how far the object will fall in 10 seconds, we substitute t = 10 into the model:
s = 15(10^2) = 1500
Therefore, the object will fall 1500 feet in 10 seconds. The answer is (E).

Solve the Problem by Writing a Variation Model