The velocity of a falling object in a vacuum is directly proportional

Question

The velocity of a falling object in a vacuum is directly proportional to the amount of time the object has been falling. If after 5 seconds an object is falling at a speed of 90 miles per hour, how fast will it be falling after 12 seconds?

A. 18 miles per hour
B. 90 miles per hour
C. 216 miles per hour
D. 1080 miles per hour
E. 5400 miles per hour

Kudos for a correct solution.

A. 18 miles per hour
B. 90 miles per hour
C. 216 miles per hour
D. 1080 miles per hour
E. 5400 miles per hour

Kudos for a correct  solution .

GMATinsight · Answer

Since Velocity is proportional to Time

Velocity =k*Time  where k is the constant of proportionality

Time  = 5 seconds
Velocity = 5k = 90 miles per Hour
i.e. k = 18

i.e. The relation between Velocity and Time becomes

Velocity =18*Time

Time  = 12 seconds

Velocity = 18*12 = 216 miles per hour

Answer: Option C

balamoon · Answer

Solution -

Given that, Velocity ∝ Time

V1/V2 = T1/T2 --> 90/V2 = 5/12------> V2=18*12 = 216 miles per hour
ANS C

chetan2u · Answer

V=kT..
90=k*5..
k=18
now v=12*18=216..
ans C

adityadon · Answer

V=KT .. 
90 = k *5

HEnce k= 18 . this is constant 
 
V=18T
= 18 * 12 = 216 miles/hr

Option C

ENGRTOMBA2018 · Answer

Given, V = k.t , V= velociy in miles/hour , k = proportionality constant, t=time in hours.

After 5 seconds,  V_5 =k*5

Thus, k = 90*3600/5 , factor of 3600 to convert 5 seconds to hours.

Now, Velocity after 12 seconds =  V_{12} = k*\frac{12}{3600} = \frac{(90*3600*12)}{(3600*5)} =216 miles per hour. C is the correct answer.

EMPOWERgmatRichC · Answer

Hi All,

The answer choices are 'spread out' enough that we can actually avoid a calculation-heavy approach.

We're told that the velocity of an object is directly proportional to how much time the object has been falling, which means that there is a 'constant' in the calculation. We're also told that an object that's been falling for 5 seconds is moving at 90 miles per hour. We're asked how fast that object would be moving after 12 seconds.

Since we're dealing with a proportion, and we're "slightly more than doubling" the time, we'll end up "slightly more than doubling" the speed. There's only one answer that's slightly more than double 90 miles per hour.

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

KS15 · Answer

After 5 seconds, object is falling @90 miles per hour
Therefore, in 1 second it will fall @90/5=18 miles per hours
And, in 12 seconds it will fall @18*12=216 miles per hour
Answer C

ENGRTOMBA2018 · Answer

That was an interesting approach. It does teach that GMAT is not looking for detailed or elegant solutions to the problems (Q or V) but something that can be logically inferred and that can save the time.

kanigmat011 · Answer

Option C is correct
V=kT..
90=k*5..
k=18
now v=12*18=216.

EMPOWERgmatRichC · Answer

Hi Engr2012,

You might be surprised at how often GMAT prompts can be approached in more than one way. Since the Quant section of the GMAT is not (strictly speaking) a "math test", keeping your eyes open to all of the information you're given (the patterns, how the answer choices are designed, etc.) can really make answering questions (and by extension, dealing with the overall Test Day 'event') easier to deal with. These same design 'shortcuts' actually appear throughout the Test, including in the Verbal section.

GMAT assassins aren't born, they're made,
Rich

ENGRTOMBA2018 · Answer

Rich,

I couldnt agree more with your observation. The first time I gave my GMAT, my highly math and physics oriented engineering background didnt allow me to let go of approaches that would have been perfect had GMAT been a theory based test. I did learn my lesson the 2nd time around but getting a 49 was a bummer. I am targeting another shot at GMAT to atleast get a Q50.

EMPOWERgmatRichC · Answer

Hi Engr2012,

With a 690/Q49, you have a great GMAT score (it's just shy of the 90th percentile overall), so you can comfortably apply to any Business Schools that interest you. Since you've mentioned that you're planning to take the GMAT again, I have to ask what your exact goals are...

If you're looking to push your score into the mid-700s, then you should be spending your time on the Verbal section. 
If you're just looking for a Q50-Q51, then WHY do you think you *need* that score? Are you planning on going into Finance?

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

Because the velocity and the time spent falling are directly proportional, you can simply set the ratio of the “before” velocity and time to the “after” velocity and time:

\frac{v_1}{w_1}=\frac{v_2}{w_2}

\frac{(90 \ mph)}{(5 \ sec)} = \frac{v_2}{(12 \ sec)}

v_2=\frac{90*12}{5}=216  mph.

Answer: C.

SamsterZ · Answer

I choose answer C as well!

I just divided 90m/ph by 5 sec (= 18) and then this 18 x 12 = 216.

Nipungupta9081 · Answer

We can also do this another way

We know 2 things are directly proportional to each other that means if we increase X by 2 , Y will also increase.
since 5 seconds it travels 90 seconds.
in 10 seconds = 90 + 90 = 180
next we see option close to 180 which is 216

Answer C

arigiurovic · Answer

hi, why we did not convert time into hours? can we still solve it even if the speed is in miles per hour and time in seconds?I'm confused... thank u

arigiurovic · Answer

hi, why we did not convert time into hours? can we still solve it even if the speed is in miles per hour and time in seconds?I'm confused... thank u

EMPOWERgmatRichC · Answer

Hi arigiurovic,

The prompt tells us that the speed is DIRECTLY PROPORTIONAL to the time spent falling. This means that the individual units of the ratio can be anything as long as the same units are on both sides of the equation. Since both sides of the equation use "seconds", there's no need to convert those measurements into hours - since we already have the proportion (re: 5 to 12). At this point, we actually don't have to do that much more math; we know that we're dealing with a proportion, and we're "slightly more than doubling" the time, so we'll end up "slightly more than doubling" the speed. There's only one answer that's slightly more than double 90 miles per hour.

GMAT assassins aren't born, they're made,
Rich

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The velocity of a falling object in a vacuum is directly proportional

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