It is currently 24 Oct 2020, 13:20

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

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

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 13671
Followers: 305

Kudos [?]: 3527 [0], given: 12608

An object thrown directly upward is at a height of h feet af [#permalink]  10 May 2020, 13:16
Expert's post
00:00

Question Stats:

57% (01:41) correct 42% (01:27) wrong based on 77 sessions
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

Kudos for the right solution and explanation
[Reveal] Spoiler: OA

_________________

Do you want all the GRE Prep Club resources at a glance (sort of ) ?? Look at GRE Prep Club Official LinkTree page

Do you want all the GRE Prep Club FREE resources in one spot ?? Look at Free GRE Materials - Where to get it!! (2020]

Do you want to know the GRE score in the Top 25 BS in 7 continents ?? Look at here The GRE average score at Top 25 Business Schools 2020 Ed.

Need Practice 20 Free GRE Quant Tests available for free with 20 Kudos

GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

GRE Instructor
Joined: 10 Apr 2015
Posts: 3871
Followers: 158

Kudos [?]: 4644 [1] , given: 70

Re: An object thrown directly upward is at a height of h feet af [#permalink]  10 May 2020, 13:56
1
KUDOS
Expert's post
Carcass 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

Kudos for the right solution and explanation

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

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.

Founder
Joined: 18 Apr 2015
Posts: 13671
Followers: 305

Kudos [?]: 3527 [0], given: 12608

Re: An object thrown directly upward is at a height of h feet af [#permalink]  10 May 2020, 14:01
Expert's post
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!

_________________

Do you want all the GRE Prep Club resources at a glance (sort of ) ?? Look at GRE Prep Club Official LinkTree page

Do you want all the GRE Prep Club FREE resources in one spot ?? Look at Free GRE Materials - Where to get it!! (2020]

Do you want to know the GRE score in the Top 25 BS in 7 continents ?? Look at here The GRE average score at Top 25 Business Schools 2020 Ed.

Need Practice 20 Free GRE Quant Tests available for free with 20 Kudos

GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Manager
Joined: 07 Aug 2016
Posts: 59
GRE 1: Q166 V156
Followers: 0

Kudos [?]: 43 [1] , given: 3

Re: An object thrown directly upward is at a height of h feet af [#permalink]  11 May 2020, 05:54
1
KUDOS
Given -16 (t-3)^2 + 150 and that the question is asking for maximum height, the maximum height occurs at t = 3 to zero out the - 16 (t - 3)^2

Maximum height = - 16 (3-3)^2 + 150 = 150

Now what happens after it reaches maximum height and continues for another 2 seconds, in addition to the 3 seconds to reach maximum height?

-16 (5-3)^2 + 150 = -16 (2^2) + 150 = - 16 * 4 + 150 = - 64 + 150 = 86
Intern
Joined: 24 Jan 2020
Posts: 24
Followers: 0

Kudos [?]: 26 [1] , given: 2

Re: An object thrown directly upward is at a height of h feet af [#permalink]  11 May 2020, 06:43
1
KUDOS
Equation for height of object h = 150 - 16$$(t-3)^2$$

The maximum height h the object can travel will occur only when the term 16$$(t-3)^2$$ is zero

Hence t-3 = 0 which makes t=3

Maximum height is reached when t=3

So the time which is 2 secs after maximum height = 3 + 2 = 5

Height at 5 secs = 150 - 16$$(5 - 3)^2$$ = 86

Intern
Joined: 07 Apr 2020
Posts: 6
Followers: 0

Kudos [?]: 7 [1] , given: 2

Re: An object thrown directly upward is at a height of h feet af [#permalink]  12 Oct 2020, 19:48
1
KUDOS
The question can be rewritten as: h = 150 - 16 (t-3)^2

As (t-3)^2 always greater than 0, so -16(t-3)^2 =< 0, so 150 - 16 (t-3)^2 =< 150, so the maximum height will be 150 when (t-3)^2 = 0, which means t = 3

The question asked at the time of 2 seconds after the max height, therefore t'= 3+2 = 5. Apply to the equation, we have:

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

Re: An object thrown directly upward is at a height of h feet af   [#permalink] 12 Oct 2020, 19:48
Display posts from previous: Sort by