help understanding use of Ratios

[Addallat]

Q:

An object is dropped from the top of a meteor crater to the surface of the moon. How many times father does it fall during its 2nd second of flight than during its 1st second? (Note: in the choices below, g stands for the magnitude of the free-fall acceleration near the surface of the moon.)

A. 2
B. 3
C. 2g
D. 3g


My approach: assuming that it drops from rest Vo = zero so I can use x = 1/2(g)(t^2)


for the 1st second: x = 1/2g

for the 2nd second: x = 4/2g


So my question is why can't I just stop at

4/2g - 1/2g = 3/2g


My brain is registering this as when t= 2 seconds the object falls 3/2 times further than when t = 1 second


I can't see why a ratio is needed

answer is D

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[FeinMS]

Shouldn't it be B? because (3g/2)/(1g/2)=3?

 

[chem4ever]

Q:

An object is dropped from the top of a meteor crater to the surface of the moon. How many times father does it fall during its 2nd second of flight than during its 1st second? (Note: in the choices below, g stands for the magnitude of the free-fall acceleration near the surface of the moon.)

A. 2
B. 3
C. 2g
D. 3g


My approach: assuming that it drops from rest Vo = zero so I can use x = 1/2(g)(t^2)


for the 1st second: x = 1/2g

for the 2nd second: x = 4/2g


So my question is why can't I just stop at

4/2g - 1/2g = 3/2g


My brain is registering this as when t= 2 seconds the object falls 3/2 times further than when t = 1 second


I can't see why a ratio is needed

answer is D

They don't want to know how muuch farther it fell in the 2nd second than in the 1st second. They want to know how many TIMES the distance it fell in the first second did it fall in the 2nd second.

In the first second it fell:

x = 1/2g

In 2 seconds (both the first AND 2nd second) it fell:

x = 1/2g(2)^2 = 4/2g

Which means that in the 2nd second alone it fell:

4/2g - 1/2g = 3/2g

So in the first second, it falls 1/2g and in the 2nd second it falls 3/2g.

How many times the distance it fell in the first second is the distance it fell in the 2nd second?

In other words, how many times 1/2g is 3/2g?

The answer should be 3. Not sure where they are getting 3g from.