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

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

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Founder
Joined: 18 Apr 2015
Posts: 12608
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Kudos [?]: 3169 [0], given: 11654

Re: An object thrown directly upward is at a height of h feet af [#permalink]  24 Jul 2020, 07:13
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Re: An object thrown directly upward is at a height of h feet af [#permalink]  24 Jul 2020, 07:33
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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
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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
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