height

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CITI29: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Tue Mar 18, 2008 9:28 am; Thanked: 2 times

by CITI29 » Tue Aug 12, 2008 1:56 pm

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

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Source: Beat The GMAT — Problem Solving | Tue Aug 12, 2008 1:56 pm

sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

by sudhir3127 » Tue Aug 12, 2008 8:52 pm

The object reaches maximum height at t=3 seconds.

At t=3+2=5 seconds ( 2 seconds later)

h = [-16*(5-3)*2] + 150 = [-16*4] +150 = 86 feet.

Answer is B.

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CITI29: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Tue Mar 18, 2008 9:28 am; Thanked: 2 times

by CITI29 » Wed Aug 13, 2008 6:26 am

How do u know object reaches its max height in 3 seconds?

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santa_dem: Senior | Next Rank: 100 Posts; Posts: 48; Joined: Fri Aug 08, 2008 4:44 am; Thanked: 4 times; GMAT Score:750

by santa_dem » Wed Aug 13, 2008 7:11 am

I didn't get the 3 seconds either.

Yes, when t=3 h=150, but what if t=1, then h= -16*(-2)*2+150=216

or, if t=2, h=182.

I would agree to "h is max when t=3" if it were |t-3| instead of (t-3), or (t-3)^2 instead of (t-3)2.

Could someone please explain.

Thanks.

Last edited by santa_dem on Wed Aug 13, 2008 7:36 am, edited 1 time in total.

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anksbhandari: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Wed Apr 30, 2008 11:05 am; Location: India

by anksbhandari » Wed Aug 13, 2008 7:19 am

i think this question is wrongly framed

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GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: height

by Ian Stewart » Wed Aug 13, 2008 8:47 am

CITI29 wrote: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

The equation is surely supposed to read:

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

i.e. the 2 should be an exponent. If you rewrite it as

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

you can see that we want (t-3)^2 to be as small as possible to make h as large as possible- that is, we want t to be equal to 3 for maximum height. Then to answer the question, we just need to plug in t = 5.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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