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

Redeem

An object thrown directly upward

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 103
Joined: Mon May 18, 2009 9:47 am
Thanked: 19 times

by raleigh » Sun Jun 14, 2009 4:03 pm
This isn't a GMAT problem, this is a calculus problem. We know that when an object reaches it's maximum height, it's velocity is zero. So to find the time the object is at it's maximum height, we take the derivative and set it equal to zero.

h'(t) = -32(t-3)

Set it equal to zero and solve for t and we find t = 3. 2 seconds after this time, t = 5.

We want to know the height at t=5. This is h(5) = -16(5-3)^2 + 150 = -16*4 + 150 = -64 + 150 = 86.

The answer is B.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 472
Joined: Sun Mar 29, 2009 6:54 pm
Thanked: 56 times

Re: An object thrown directly upward

by ssmiles08 » Sun Jun 14, 2009 4:20 pm
kakkupikku 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

OA:B
The question is for some reason worded wierdly to me but I think the main point is that h = height in feet, t = time in seconds

The equation of height at t seconds is given as -16 (t - 3)^2 + 150

Now we want to find the height 2 seconds after it has reached its max height.

Max height will be reached when t = 3:

when t = 3, (-16*0) = 0 and you are not subtracting anything from the height of 150.

Thus when t = 3, h = 150 (MAX height)

2 sec after 3 is t = 5

so -16*(2)^2 +150

-64 + 150 = 86

(B)
Top
Legendary Member
Posts: 752
Joined: Sun May 17, 2009 11:04 pm
Location: Tokyo
Thanked: 81 times
GMAT Score:680

by tohellandback » Sun Jun 14, 2009 6:01 pm
than answer should be B
since (t-3)^2 is always positive ,so it will be minimum when t=3

after two second i.e 3=2=5 seconds
putting t=5 in the eq

h=-64+150
h=86
The powers of two are bloody impolite!!
Top
Master | Next Rank: 500 Posts
Posts: 103
Joined: Mon May 18, 2009 9:47 am
Thanked: 19 times

by raleigh » Sun Jun 14, 2009 6:46 pm
Very intuitive way to look at the problem. Good work. I see any sort of projectile motion and I instinctively think calculus ;-)
Top
Legendary Member
Posts: 752
Joined: Sun May 17, 2009 11:04 pm
Location: Tokyo
Thanked: 81 times
GMAT Score:680

by tohellandback » Sun Jun 14, 2009 6:51 pm
raleigh wrote:Very intuitive way to look at the problem. Good work. I see any sort of projectile motion and I instinctively think calculus ;-)
Lucky you..coz when i see time, distance, height, length, I immediately draw a line and start looking for who is going where :roll:
The powers of two are bloody impolite!!
Top
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Tue Jan 27, 2009 5:44 am

by kakkupikku » Sun Jun 14, 2009 10:25 pm
This is a gmat question. Was in set 26 of math Question #21.

Wow, great soln !!! I missed the "after reaching max height part" when i solved it.. thanks !!!
Top
Post new topic Post Reply
• Page 1 of 1