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Equations

This topic has 2 expert replies and 4 member replies
vinay1983 Legendary Member
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Equations

Post Sun Sep 01, 2013 9:46 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) 166

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Java_85 Master | Next Rank: 500 Posts
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Top Reply
Post Mon Sep 02, 2013 8:30 am
vinay1983 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) 166
Equations with the power of two are U shape curves! The peak of this U shape curves is the only point that the Derivative is Zero i.e. d/dt (-16(t- 3)^2 + 150)==0 ==> d/dt(t^2-6t+9)==0 ==> 2t-6=0 ==> t=3 is the time that We're at the peak of this U shape Curve, 2 seconds after peak==> t=5 ==> h(5)=86 ==> B

Since it's a U shape curve at time t=1 also the height is 86. it does not matter 2 seconds before getting to peak or after! for both the height is always the same for quadratic equations.

Hope this helps.

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Top Reply
Post Mon Sep 02, 2013 9:30 am
Java_85 wrote:
vinay1983 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) 166
Equations with the power of two are U shape curves! The peak of this U shape curves is the only point that the Derivative is Zero i.e. d/dt (-16(t- 3)^2 + 150)==0 ==> d/dt(t^2-6t+9)==0 ==> 2t-6=0 ==> t=3 is the time that We're at the peak of this U shape Curve, 2 seconds after peak==> t=5 ==> h(5)=86 ==> B

Since it's a U shape curve at time t=1 also the height is 86. it does not matter 2 seconds before getting to peak or after! for both the height is always the same for quadratic equations.

Hope this helps.
Your solution is 100% correct, Java_85, but I want to point out to people (who may be experiencing painful flashbacks from Calculus 101 Smile) that the GMAT does not require any knowledge of Calculus. Sure, there may be the occasional question that can be solved using derivatives or integral, but the same question will also be solvable using non-Calculus approaches)

If we rewrite the formula as h = 150-16(t-3)², we can see that, in order to MAXIMIZE the value of h we must 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 seconds.

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
Answer: B

Cheers,
Brent

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Java_85 Master | Next Rank: 500 Posts
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Post Mon Sep 02, 2013 8:30 am
vinay1983 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) 166
Equations with the power of two are U shape curves! The peak of this U shape curves is the only point that the Derivative is Zero i.e. d/dt (-16(t- 3)^2 + 150)==0 ==> d/dt(t^2-6t+9)==0 ==> 2t-6=0 ==> t=3 is the time that We're at the peak of this U shape Curve, 2 seconds after peak==> t=5 ==> h(5)=86 ==> B

Since it's a U shape curve at time t=1 also the height is 86. it does not matter 2 seconds before getting to peak or after! for both the height is always the same for quadratic equations.

Hope this helps.

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Post Mon Sep 02, 2013 9:30 am
Java_85 wrote:
vinay1983 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) 166
Equations with the power of two are U shape curves! The peak of this U shape curves is the only point that the Derivative is Zero i.e. d/dt (-16(t- 3)^2 + 150)==0 ==> d/dt(t^2-6t+9)==0 ==> 2t-6=0 ==> t=3 is the time that We're at the peak of this U shape Curve, 2 seconds after peak==> t=5 ==> h(5)=86 ==> B

Since it's a U shape curve at time t=1 also the height is 86. it does not matter 2 seconds before getting to peak or after! for both the height is always the same for quadratic equations.

Hope this helps.
Your solution is 100% correct, Java_85, but I want to point out to people (who may be experiencing painful flashbacks from Calculus 101 Smile) that the GMAT does not require any knowledge of Calculus. Sure, there may be the occasional question that can be solved using derivatives or integral, but the same question will also be solvable using non-Calculus approaches)

If we rewrite the formula as h = 150-16(t-3)², we can see that, in order to MAXIMIZE the value of h we must 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 seconds.

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
Answer: B

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
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Post Sun Sep 01, 2013 10:47 pm
Hi vinay1983,

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

You'll have the correct answer: -16(5-3)^2 + 150 = -64 + 150 = 86

GMAT assassins aren't born, they're made,
Rich

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sanjoy18 Senior | Next Rank: 100 Posts Default Avatar
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Post Sun Sep 01, 2013 10:06 pm
its B for me

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