It is currently 14 Aug 2020, 09:29

### 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: 12642
Followers: 269

Kudos [?]: 3178 [0], given: 11677

An object thrown directly upward is at a height of h feet af [#permalink]  24 Jul 2020, 07:12
Expert's post
00:00

Question Stats:

56% (01:25) correct 43% (00:38) wrong based on 16 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
[Reveal] Spoiler: OA

_________________

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.

Founder
Joined: 18 Apr 2015
Posts: 12642
Followers: 269

Kudos [?]: 3178 [0], given: 11677

Re: An object thrown directly upward is at a height of h feet af [#permalink]  24 Jul 2020, 07:13
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!

For more GRE Quant Theory and Practice, see

GRE Prep Club - MATH Book for the GRE Exam
_________________

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: 3677
Followers: 142

Kudos [?]: 4249 [1] , given: 67

Re: An object thrown directly upward is at a height of h feet af [#permalink]  24 Jul 2020, 07:33
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

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
_________________

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

Intern
Joined: 15 Mar 2020
Posts: 16
Followers: 0

Kudos [?]: 14 [0], given: 7

Re: An object thrown directly upward is at a height of h feet af [#permalink]  27 Jul 2020, 12:06
h = -16(t - 3)^2 + 150
to find t at which h is max we need to take a derivative with respect to t and equalise it to 0
(-16t^2 + 96t -16*9 + 150)'=0
-16*2t + 96=0
t = 3
so h is max after 3 seconds.
2 srconds after gives as 5 seconds
h(5) = -16(5-3)^2+150=86
Re: An object thrown directly upward is at a height of h feet af   [#permalink] 27 Jul 2020, 12:06
Display posts from previous: Sort by