BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

set 26 q 21

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 144
Joined: Fri Apr 13, 2007 2:25 am

set 26 q 21

by radhika1306 » Tue Sep 11, 2007 10:57 am
An object thrown directly upward is at a height of h feet after t seconds, where h = -16 (t - 3)2 +
150. At what height, in feet, is the object 2 seconds after it reaches its maximum height?
A. 6
B. 86
C. 134
D 150
E. 214
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 321
Joined: Tue Aug 28, 2007 5:42 am
Thanked: 1 times

by kajcha » Tue Sep 11, 2007 12:03 pm
The object will reach its max height when t=3.

2 secs after means 5 sec after

h = -16(5-3)2 + 150 = -64 + 150 = 86 ANS B
Top
Master | Next Rank: 500 Posts
Posts: 258
Joined: Mon Aug 27, 2007 12:43 pm
Thanked: 15 times

by ri2007 » Tue Sep 11, 2007 12:34 pm
Hi

I am not sure I understand this. In the equation given
h = -16 (t - 3)2 + 150

The maximum height will be reached with the value of t is the smallest. so for instance if we assume t = 3 then the max height the obejct will achieve is

-16 (0)2 +150 = 0

However if t =1 (just an ex) the height achieved would be

-16 (1-3)2 +150 = -16(-2)2 +150 = 64 +150

What am I missing? How did u get that max height is achieved after 3 secs?

thanks
Top
Master | Next Rank: 500 Posts
Posts: 321
Joined: Tue Aug 28, 2007 5:42 am
Thanked: 1 times

by kajcha » Tue Sep 11, 2007 1:05 pm
ri2007, you are correct.. max height will be reached when t = 1. So ans would be 150.. thanks a ton...
another lesson for me to read the question properly.
Top
Master | Next Rank: 500 Posts
Posts: 258
Joined: Mon Aug 27, 2007 12:43 pm
Thanked: 15 times

by ri2007 » Tue Sep 11, 2007 1:17 pm
Well actually kajcha

I am not sure how to read this question. Maximum height will be reached with the smalles value of t. It cant be 0. So if we assume we measure the heright agter 0.00001 sec that will be the max height.

May be some one else can comment on this as well??
Top
Senior | Next Rank: 100 Posts
Posts: 71
Joined: Wed Aug 22, 2007 12:29 pm
Location: USA
Thanked: 12 times
Followed by:1 members

by wizardofwashington » Tue Sep 11, 2007 2:28 pm
ri2007 wrote:Hi

I am not sure I understand this. In the equation given
h = -16 (t - 3)2 + 150

The maximum height will be reached with the value of t is the smallest. so for instance if we assume t = 3 then the max height the obejct will achieve is

-16 (0)2 +150 = 0

However if t =1 (just an ex) the height achieved would be

-16 (1-3)2 +150 = -16(-2)2 +150 = 64 +150

What am I missing? How did u get that max height is achieved after 3 secs?

thanks
Just curious to know why can't we consider t =0? Isn't that when the object would be at its highest (96+150 = 246).

Also, the question asked "At what height, in feet, is the object 2 seconds after it reaches its maximum height?", which means T=2?

Grrrrr.. This question is driving me crazy already..Please help..Thanks
A falling tree resounds... but a forest grows in silence...
Top
Senior | Next Rank: 100 Posts
Posts: 71
Joined: Wed Aug 22, 2007 12:29 pm
Location: USA
Thanked: 12 times
Followed by:1 members

by wizardofwashington » Tue Sep 11, 2007 3:59 pm
Now this starting to get really confusing..Too exhausted for my own good trying to solve this problem (For sure I'll make a guees if this problem appears on the real GMAT)..
Now, to answer the anonymous poster, for argument sake, let me agree with your statement that when T=0 the ball has not left your hand. You are making this assumption, the throwing happens when t=0. But how come the h is not zero if the ball hasn't left your hand. Plugging in the value t=0, how come I end up getting the height as 246ft. That's what baffles me. I'm starting to feel that the approach to this problem, at least from my end, has been fundamentally flawed.

Here what ri2007 posted makes sense. With t =1, the object would have reached its maximum height of 214ft. The question asked "At what height, in feet, is the object 2 seconds after it reaches its maximum height?" can then be interpreted as t=3, which then makes h=150ft, leading to answer choice D.

The trick, I assume, here is to determine when the height is at the maximum, which happens, only when t=1...Before I go crazy can some of the other smartest (read as moderators/owners) be called in to look at this problem since they have been around here long enough to have come across a solution to this kinda problem..Mods/owners, could you please step forward and help.....
A falling tree resounds... but a forest grows in silence...
Top
Master | Next Rank: 500 Posts
Posts: 258
Joined: Mon Aug 27, 2007 12:43 pm
Thanked: 15 times

by ri2007 » Wed Sep 12, 2007 10:33 am
radhika1306

can you pls check the question and confirm if it is
h= -16 (t-3)^2 +150 OR

h= -16 (t-3)2 +150


Asked Samir Pandey to take a look at this question and he correctly pointed out it would make much more sence if it was the

h= -16 (t-3)^2 +150 instead of h= -16 (t-3)2 +150 as is currently given in ur post.

Thanks
Top
User avatar
Legendary Member
Posts: 986
Joined: Wed Dec 20, 2006 11:07 am
Location: India
Thanked: 51 times
Followed by:1 members

by gabriel » Wed Sep 12, 2007 12:50 pm
.. i guess its the lack of sleep ( its 2:15 am over here) .. but this question makes absolutely no sense ..

..the equation given for the height "h" just cant be true .. if the question was that the ball was dropped from a height then it would make some sense..

@ ri2007.. h cannnot be equal to =-16(t-3)^2+150 as well.. because at t = 0 the height should be equal to 0 and not 6 feet as it would be if h = -16(t-3)^2+150 ..

.. radhika please do check the question again ... if there is no mistake from your side then i guess everyone should just ignore this question ..

.. well, off to sleep ..
Top
Senior | Next Rank: 100 Posts
Posts: 71
Joined: Wed Aug 22, 2007 12:29 pm
Location: USA
Thanked: 12 times
Followed by:1 members

A better explanation - from Pagalguy.com

by wizardofwashington » Wed Sep 12, 2007 2:10 pm
Guys, I got the same question posted on PagalGuy.com and what I got made more sense. It is a very logical explanation and probably will help us conclude that this is one whacky question. Thanks to "esh.nil" an ExpertPagal, who came up with this very convincing solution.

Here it goes:
---------------------------------------------------------------------------
I am sure this will never feature in cat..(Who knows)
the approach goes like this,
the max height tha the stone can reach is at t=3sec = 150m
after it reaches the max height, then it is at the mercy of the gravity. so it accelarates down towards the earth at 9.8 m/s^2
so vel at the first second is v = at = 9.8m/s = 32 feet/sec
so vel at the seconnd second = 19.6 m/s = 64 feet/sec
so the distance the obj is from the ground is 150-(96) = 54 feet..

I guess the answer choices are wrong in the question...
I guess the person who prepared the answer choice assumed that the vel is same for the first and second sec and hence 150-(32+32) = 86.... But this is obviously wrong.. since the vel is not same until terminal velocity is reached.
Hope my approach is correct, been long since i studied my physics lessons
-------------------------------------------------------------------------------------
A falling tree resounds... but a forest grows in silence...
Top
Master | Next Rank: 500 Posts
Posts: 460
Joined: Sun Mar 25, 2007 7:42 am
Thanked: 27 times

by samirpandeyit62 » Wed Sep 12, 2007 9:34 pm
Hi All,
Gabriel you wrote:

@ ri2007.. h cannnot be equal to =-16(t-3)^2+150 as well.. because at t = 0 the height should be equal to 0 and not 6 feet as it would be if h = -16(t-3)^2+150

this is perfectly rational as the formula is meant to give the height of the object at a given time.

when t=0 then if the object is thrown from the ground upwards, then we can assume that h =0

but if it is thrown by some entilty upwards then that entity may have a height of 6 feet, i.e the object is held by a person 6 feet tall who thows it
This is rational as the object is in his hand i.e at 6 feet height at t =0, hence h=6 feet.

However if we assume that formula is h=-16(t-3)2+150

the at t=0 we have height = 246 feet at t=1 the height = 214 & it will decrease as t increases so means that "some one standing on some entity like a cliff throwed it directly down"

This would voilate the question i.e. "An object thrown directly upward "

so my ans 86 & the correct formula IMO should be h=-16(t-3)^2+150
Regards
Samir
Top
Master | Next Rank: 500 Posts
Posts: 460
Joined: Sun Mar 25, 2007 7:42 am
Thanked: 27 times

by samirpandeyit62 » Wed Sep 12, 2007 11:17 pm
As I was in a hurry to move somewhere, I could not add a couple of lines to the my post above,

This formula reperesents the relationship between height & time of the object, so in this if we enter value of time we can get height of the object at that time,

Pls remember this is a formula for a mutally exclusive (customised) situation, i.e this is not a general formula, so to find the height of the object we cannot use any general formula, but only this one.

coz we dont know the objects trajectory, In his post wizardofwashington mentioned that we can use gravity to get the soln, this is true only if the object was thrown VERTICALLY upwards, I dont think that directly upwords means exactly the same, The objects trajectory may be in the shape of a Bell curve ( i.e like a golf ball is hit directly upwards (imagine an opposite V)

In this case the force applied on the object would have 3 components when it rises up 1 i.e vertical, causing the object to accelerate vertically & horizontal causing it to accelerate horizontally & gravity pulling it down

Now when the object reaches its max height & falls back the vertical components of the force driving the object upwards would be zero now gravity would be the major component accelerating it downwards but still some horizontal component componet of force would exist, causing the object to move horizotally as well vertically downwords (thats way we have opposite V curve)

So to get the exact height here we would need Vector Calculus.

Pardon me for this unnessary explanation, but my intent was to just clarify things so that if we extend the scope of the question too much outside , then the ans would never be correct (as I dont think this much is required on the GMAT).

So IMO whoever made this formula did the required calculus & calulated the height of the object at various points of time & then created this formula for us to solve for height using time.

Thanks
Regards
Samir
Top
User avatar
Legendary Member
Posts: 986
Joined: Wed Dec 20, 2006 11:07 am
Location: India
Thanked: 51 times
Followed by:1 members

by gabriel » Thu Sep 13, 2007 9:33 am
samirpandeyit62 wrote:Hi All,
Gabriel you wrote:

@ ri2007.. h cannnot be equal to =-16(t-3)^2+150 as well.. because at t = 0 the height should be equal to 0 and not 6 feet as it would be if h = -16(t-3)^2+150

this is perfectly rational as the formula is meant to give the height of the object at a given time.

when t=0 then if the object is thrown from the ground upwards, then we can assume that h =0

but if it is thrown by some entilty upwards then that entity may have a height of 6 feet, i.e the object is held by a person 6 feet tall who thows it
This is rational as the object is in his hand i.e at 6 feet height at t =0, hence h=6 feet.

However if we assume that formula is h=-16(t-3)2+150

the at t=0 we have height = 246 feet at t=1 the height = 214 & it will decrease as t increases so means that "some one standing on some entity like a cliff throwed it directly down"

This would voilate the question i.e. "An object thrown directly upward "

so my ans 86 & the correct formula IMO should be h=-16(t-3)^2+150
oh come on!! .. you are just being pedantic over here .... I mean i can go a little further and say that if we assume the guy is 6 feet tall and holds the ball at the head level then to throw the ball he needs to swing his hands downwards thereby at t=1 the level of ball will be less than 6 .. did that make any sense .. well, it was not supposed to ..

u may well be right about the equation .. but i still stick to my point that this is a bad question ...because it forces u to make a number of assumptions based on some very ambiguous material ...

Regards :)
Top
Master | Next Rank: 500 Posts
Posts: 144
Joined: Fri Apr 13, 2007 2:25 am

by radhika1306 » Thu Sep 13, 2007 9:35 am
sorry for the confusion guys
it's

h=-16(t-3)^2+150
Top
Master | Next Rank: 500 Posts
Posts: 460
Joined: Sun Mar 25, 2007 7:42 am
Thanked: 27 times

by samirpandeyit62 » Thu Sep 13, 2007 10:02 am
Hi Gabreil,
This one was not the only one, I've now seen several questions like these which make no sense as you rightly pointed out, but I believe that my job is to solve them to get the correct answer :D even if they dont make any sense :? , What say u Gabriel. By the way you were awake till 2:15 am, was it something to do with the 20-20 Cricket Wordcup
Regards
Samir
Top
Post new topic Post Reply