distance freefalling body travels varies as the square of the time it's been falling. If a object falls 320m in 8secs, how far will it fall in 3 secs?

Question

Explain your answer please.

Answer 1

Object in free fall is accelerating as it is falling. That is why the distance it travels varies as the square of the time it's been falling.

 

Derive the gravity constant from the original information:

d = .5 g t²

320m = .5 (8s)² g

320m = .5(64s²)g

320m = 32s²g

g = 320m/32s²

g = 10m/s²

 

Plug in information for 3 seconds:

 

d = .5 (10m/s²)(3s)²

d = .5(10m/s2)(9s²)

d = .5(90m)

d = 45m

Answer 2

ANSWER: It will travel 45m in 3 seconds.

 

When two quantities directly vary, then their quotients will always be the same number.

 

In this problem, we have 320m/(8^2)=5. So the quotient of the distance traveled divided by the square of the time will always be 5.

 

So to figure out the distance fallen in 3 secs, we set up a new equation and set it equal to 5 where the x is equal to the distance fallen.

 

x/(3^2)=5

x/9=5

x=45

 

The distance traveled in 3 seconds will be 45m.