Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 19 Jul 2019, 05:25 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # An object thrown directly upward is at a height of h feet

Author Message
TAGS:

### Hide Tags

Manager  Joined: 12 Oct 2009
Posts: 139
An object thrown directly upward is at a height of h feet  [#permalink]

### Show Tags

7
122 00:00

Difficulty:   45% (medium)

Question Stats: 67% (01:47) correct 33% (01:54) wrong based on 3002 sessions

### HideShow timer Statistics 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
Math Expert V
Joined: 02 Sep 2009
Posts: 56302
Re: An object thrown directly upward is at a height of h feet  [#permalink]

### Show Tags

31
32
IEsailor 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

Given that $$h=150-16(t-3)^2$$.

In order to maximize $$h$$, we need to minimize $$16(t-3)^2$$ (since it's subtracted from 150), which means minimizing $$(t-3)^2$$. Now, since $$(t-3)^2$$ is always non-negative, then the smallest possible value of $$(t-3)^2$$ is 0, for $$t=3$$.

Two seconds later or for $$t=3+2=5$$, the height will be $$h=150-16(5-3)^2=86$$.

Hope it's clear.
_________________
Director  Joined: 01 Feb 2011
Posts: 629
Re: PS - Height of object  [#permalink]

### Show Tags

6
2
Maximum height is reached at t=3 i.e 150

2 sec's after reaching maximum height object will be in free fall mode.
=> height at t =1, is the height of the object 2 seconds after it reaches its maximum height?

substituting t=2 we have 150-16(4)
=86

##### General Discussion
Director  Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 950
Re: PS - Height of object  [#permalink]

### Show Tags

5
2
max height at t=3, 150

2 sec after t=3 means t=5.

substituting h= -64 + 150 = 86
Joined: 31 Dec 1969
Location: Russian Federation
WE: Supply Chain Management (Energy and Utilities)
Re: PS - Height of object  [#permalink]

### Show Tags

Spidy001 wrote:
Maximum height is reached at t=3 i.e 150

2 sec's after reaching maximum height object will be in free fall mode.
=> height at t =1, is the height of the object 2 seconds after it reaches its maximum height?

substituting t=2 we have 150-16(4)
=86

How you can say the max height is reached when t=3
Intern  Joined: 12 Jan 2012
Posts: 21
GMAT 1: 720 Q49 V39 Re: PS - Height of object  [#permalink]

### Show Tags

divyakatas wrote:
Spidy001 wrote:
Maximum height is reached at t=3 i.e 150

2 sec's after reaching maximum height object will be in free fall mode.
=> height at t =1, is the height of the object 2 seconds after it reaches its maximum height?

substituting t=2 we have 150-16(4)
=86

How you can say the max height is reached when t=3

Method 1: -16(t-3)^2 would reduce the value of 150 and h would be maximum when -16(t-3) ^2 = 0 ie t = 3
Method 2: using derivatives dh/dt = 0.
Manager  Joined: 21 Aug 2012
Posts: 105
Re: An object thrown directly upward is at a height of h feet  [#permalink]

### Show Tags

3
1
IEsailor 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

Hi,

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

Now, in the above expression whenever t is of any value except 3, the overall $$(t-3)^2$$ is always +ve.
and this +ve value is multiplies by -16.. Hence, this overall value is negative.

In order to make sure that max. height is reached, $$-16(t-3)^2$$ has to be positive, but it is never positive. SO a zero value will work to get the max. height.

So t has to be 3 to get $$-16 (t -3)^2$$ as zero, and obtain the maximum height.

Now, when t=3
h=150

The question asks for the height when time is 2 second after max height. After max. height, the object will fall.
So, the time will be 5 second. ( 3+2)

$$h = 150 -16(5-3)^2$$
h = 150 - 16*4
h = 150 -64
h = 86

Hence, the height will be 86 feet.

Thanks,
Jai

KUDOS if it helped..!!! _________________
MODULUS Concept ---> http://gmatclub.com/forum/inequalities-158054.html#p1257636
HEXAGON Theory ---> http://gmatclub.com/forum/hexagon-theory-tips-to-solve-any-heaxgon-question-158189.html#p1258308
Manager  B
Status: Eagles Become Vultures
Joined: 19 Jun 2014
Posts: 59
Concentration: Finance, Strategy
Schools: LBS '18 (M)
GMAT 1: 710 Q48 V39 GPA: 4
WE: Corporate Finance (Energy and Utilities)
An object thrown directly upward is at a height of h feet  [#permalink]

### Show Tags

1
First find out what height would be considered as 'maximum' given the equation:

Since 150 is a constant, find out what the product's maximum value can be. It is a product of a negative number and a squared parenthesis; this product would ALWAYS be negative UNLESS the parenthesis yields zero - this would be the point at which the product would have maximum value.

For t = 3, the expression would yield 0 + 150. Hence, the maximum possible height given by this equation would be 150 feet. Therefore, after reaching this height, the object would start falling. The 'start' time of falling would be after 3 seconds, so adding 2 seconds would be 5:

h = -16 x (5-3)^2 + 150
h = -16 x 4 + 150
h = 86
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14586
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: An object thrown directly upward is at a height of h feet  [#permalink]

### Show Tags

2
1
Hi All,

This is an example of a "limit" question. The question requires you to figure out the "maximum" height using a given equation.

You'll notice that the first part of the equation is -16(other things), so you'll subtract something from 150 except when that first part = 0

If t = 3 seconds, then you have -16(0)^2 + 150 = 150 feet

So, 150 feet is the maximum height.

We're asked for the height 2 seconds AFTER the maximum height, so plug in t = 5

-16(5-3)^2 + 150 = -64 + 150 = 86; Answer B

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin Follow
Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Director  P Status: Professional GMAT Tutor Affiliations: AB, cum laude, Harvard University (Class of '02) Joined: 10 Jul 2015 Posts: 696 Location: United States (CA) Age: 39 GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42 GRE 1: Q168 V169 WE: Education (Education) Re: An object thrown directly upward is at a height of h feet [#permalink] ### Show Tags 2 1 Attached is a visual that should help. Attachments Screen Shot 2016-05-25 at 9.42.24 PM.png [ 122.1 KiB | Viewed 30708 times ] _________________ Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching worldwide since 2002. One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V. You can download my official test-taker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y7knw7bt Date of Birth: 09 December 1979. GMAT Action Plan and Free E-Book - McElroy Tutoring Contact: mcelroy@post.harvard.edu (I do not respond to PMs on GMAT Club.) ...or find me on Reddit: http://www.reddit.com/r/GMATpreparation Intern  Joined: 28 Dec 2015 Posts: 39 Re: An object thrown directly upward is at a height of h feet [#permalink] ### Show Tags h=-16(t-3)^2+150 This further simplifies to h=-16t^2+96t+6 Now this is an downward parabola,since a is negative. The vertex or the maximum height is given by t=-b/2a or t=-96/2*-16 or t=3 seconds So at t=3 sec the max height is reached. 2 seconds later what is the height? So,t=5 sec Substitute in the height equation to get h=86 ft. Target Test Prep Representative G Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2823 Re: An object thrown directly upward is at a height of h feet [#permalink] ### Show Tags 2 IEsailor 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 We are given an equation h = –16(t – 3)^2 + 150, with the following information: h = height of h feet t = number of seconds We need to determine the height, in feet, 2 seconds after it reaches maximum height. So we first need to determine the value of t when the object's height h is the maximum. In other words, we need to determine the maximum value for this equation. We first focus on “-16(t - 3)^2”. We ascertain that (t – 3)^2 is always either positive or 0. However, when (t – 3)^2 is multiplied by –16, a negative number, the product will be negative. Thus, the best we can do is to have the expression -16(t - 3)^2 equal 0, which would yield the maximum value of –16(t – 3)^2 + 150. We can obtain this value by letting t = 3. We now know that the object reaches its maximum height at t = 3 (and the maximum height is 150 ft). However, we want the height of the object 2 seconds after it reaches the maximum height. Thus, we want the height at t = 5 since 3 + 2 = 5. Thus, we can plug in 5 for t and solve for h. h = -16(t - 3)^2 + 150 h = -16(5 - 3)^2 + 150 h = -16(2)^2 + 150 h = -16 x 4 + 150 h = -64 + 150 h = 86 Answer B _________________ # Jeffrey Miller Head of GMAT Instruction Jeff@TargetTestPrep.com See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Intern  B Joined: 07 Jul 2016 Posts: 38 Location: India Concentration: Technology, Marketing GMAT 1: 740 Q50 V41 GPA: 3.6 Re: An object thrown directly upward is at a height of h feet [#permalink] ### Show Tags ok here is what i did in the first attempt..... max height reached is 150 . 2 seconds after that h = -16(2-3)^2 + 150 = -16+150 = 134. 150-134 = 16. Where did i go wrong? EMPOWERgmat Instructor V Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14586 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: An object thrown directly upward is at a height of h feet [#permalink] ### Show Tags Hi abhibad, The equation that the prompt gives us to work with tells us the height of the ball after T seconds have elapsed. So, after 3 seconds (meaning T=3), the height of the ball is 150 feet. Two seconds AFTER that would be the 5 second 'mark' (meaning T=5). In your calculation, you plugged in T=2. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Follow Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Intern  B
Joined: 07 Jul 2016
Posts: 38
Location: India
Concentration: Technology, Marketing
GMAT 1: 740 Q50 V41 GPA: 3.6
Re: An object thrown directly upward is at a height of h feet  [#permalink]

### Show Tags

1
2 seconds after reaching the maximum height, time to reach the maximum height is 3 seconds, so after 2 seconds the fall is calculated is 134. I think i understand the flaw in my calculation the formula is from the starting point only hence it cannot be applied after reaching the maximum height.
CEO  V
Joined: 12 Sep 2015
Posts: 3848
Re: An object thrown directly upward is at a height of h feet  [#permalink]

### Show Tags

Top Contributor
1
IEsailor 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 formula h = -16 (t - 3)² + 150 allows us to determine the height of the object at any time. For what value of t is -16(t-3)² + 150 MAXIMIZED(in other words, the object is at its maximum height)?

It might be easier to answer this question if we rewrite the formula as h = 150 - 16(t-3)²
To MAXIMIZE the value of h, we need to MINIMIZE the value of 16(t-3)² and this means minimizing the value of (t-3)²
As you can see,(t-3)² is minimized when t = 3.

We want to know the height 2 seconds AFTER the object's height is maximized, so we want to know that height at 5 seconds (3+2)

At t = 5, the height = 150 - 16(5 - 3)²
= 150 - 16(2)²
= 150 - 64
= 86

RELATED VIDEO FROM OUR COURSE

_________________
Manager  B
Joined: 30 Apr 2013
Posts: 77
Re: An object thrown directly upward is at a height of h feet  [#permalink]

### Show Tags

Is this concept frequently tested in GMAT? I am finding it little difficult to understand.
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14586
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: An object thrown directly upward is at a height of h feet  [#permalink]

### Show Tags

1
Hi santro789,

This is an example of a 'limit' question - and this particular 'design' is relatively rare (you might not see it at all on Test Day). In the broader sense though, the concept isn't that difficult. You're told that there's a MAXIMUM height, so you have to think about what has to happen to achieve the highest possible height given that equation (and when you think of everything in those terms, you're really just dealing with a Number Property and using critical thinking skills - NOT 'math' skills). Even if you don't spot the pattern here, you can still 'brute force' the solution: just plug in increasing values of T until you get the answer.

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin Follow
Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Manager  P
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 106
An object thrown directly upward is at a height of h feet  [#permalink]

### Show Tags

I prepared a youtube video to explain this question. Hope you'll like it.

Check the explanation on this video
_________________ An object thrown directly upward is at a height of h feet   [#permalink] 29 Oct 2018, 06:59
Display posts from previous: Sort by

# An object thrown directly upward is at a height of h feet  