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
) 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 - Creator of GMATPrepNow.com
