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# A model rocket takes off from an elevated launch pad which is 32 feet

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Math Expert
Joined: 02 Sep 2009
Posts: 65807
A model rocket takes off from an elevated launch pad which is 32 feet  [#permalink]

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01 Jul 2020, 10:07
00:00

Difficulty:

45% (medium)

Question Stats:

65% (02:08) correct 35% (02:28) wrong based on 22 sessions

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A model rocket takes off from an elevated launch pad which is 32 feet above the ground. The rocket’s elevation is given by the function $$h(t) = −16t^2 + 64t + 32$$, where $$h(t)$$ represents the height, in feet above ground, after t seconds. At which of the following times, in seconds, is the rocket’s height 80 feet above ground?

I. 2.5
II. 3
III. 4

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

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Director
Joined: 16 Feb 2015
Posts: 657
Location: United States
A model rocket takes off from an elevated launch pad which is 32 feet  [#permalink]

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Updated on: 02 Jul 2020, 03:40
Explanation:
h(t)=−16t^2 + 64t + 32
I. 2.5
= −16(2.5)^2 + 64(2.5)+ 32
= 92

II. 3
= −16(3)^2 + 64(3)+ 32
= 80

III. 4
= −16(4)^2 + 64(4)+ 32
= 32

IMO-B

Originally posted by rajatchopra1994 on 01 Jul 2020, 10:17.
Last edited by rajatchopra1994 on 02 Jul 2020, 03:40, edited 1 time in total.
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Re: A model rocket takes off from an elevated launch pad which is 32 feet  [#permalink]

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01 Jul 2020, 10:22
Bunuel wrote:
A model rocket takes off from an elevated launch pad which is 32 feet above the ground. The rocket’s elevation is given by the function $$h(t) = −16t^2 + 64t + 32$$, where $$h(t)$$ represents the height, in feet above ground, after t seconds. At which of the following times, in seconds, is the rocket’s height 80 feet above ground?

I. 2.5
II. 3
III. 4

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

Given,
$$h(t) = −16t^2 + 64t + 32$$
=> $$−16t^2 + 64t + 32 = 80$$
=> $$−16t^2 + 64t - 48 = 0$$
Dividing the equation by (-16), we get
=> $$t^2 - 4t + 3 = 0$$
=> $$(t - 3)(t - 1) = 0$$
=> $$t = 3 or 1$$

Only II. has required value.
Thus, OA is (B).
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A model rocket takes off from an elevated launch pad which is 32 feet  [#permalink]

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Updated on: 02 Jul 2020, 03:34
at exact 80 feet above ground option II is valid and for height >80 feet 2.5 is valid
in this case option B is correct

v12345 wrote:
Bunuel wrote:
A model rocket takes off from an elevated launch pad which is 32 feet above the ground. The rocket’s elevation is given by the function $$h(t) = −16t^2 + 64t + 32$$, where $$h(t)$$ represents the height, in feet above ground, after t seconds. At which of the following times, in seconds, is the rocket’s height 80 feet above ground?

I. 2.5
II. 3
III. 4

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

Given,
$$h(t) = −16t^2 + 64t + 32$$
=> $$−16t^2 + 64t + 32 = 80$$
=> $$−16t^2 + 64t - 48 = 0$$
Dividing the equation by (-16), we get
=> $$t^2 - 4t + 3 = 0$$
=> $$(t - 3)(t - 1) = 0$$
=> $$t = 3 or 1$$

Only II. has required value.
Thus, OA is (B).

Originally posted by Archit3110 on 01 Jul 2020, 21:13.
Last edited by Archit3110 on 02 Jul 2020, 03:34, edited 1 time in total.
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Re: A model rocket takes off from an elevated launch pad which is 32 feet  [#permalink]

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02 Jul 2020, 02:48
Archit3110 wrote:
v12345

what you have determined is the value when height is 80 feet , where question has asked ; At which of the following times, in seconds, is the rocket’s height 80 feet above ground?

Only option A; is valid where H = 92 feet

v12345 wrote:
Bunuel wrote:
A model rocket takes off from an elevated launch pad which is 32 feet above the ground. The rocket’s elevation is given by the function $$h(t) = −16t^2 + 64t + 32$$, where $$h(t)$$ represents the height, in feet above ground, after t seconds. At which of the following times, in seconds, is the rocket’s height 80 feet above ground?

I. 2.5
II. 3
III. 4

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

Given,
$$h(t) = −16t^2 + 64t + 32$$
=> $$−16t^2 + 64t + 32 = 80$$
=> $$−16t^2 + 64t - 48 = 0$$
Dividing the equation by (-16), we get
=> $$t^2 - 4t + 3 = 0$$
=> $$(t - 3)(t - 1) = 0$$
=> $$t = 3 or 1$$

Only II. has required value.
Thus, OA is (B).

Hi Archit3110,
Could you please explain the difference, because I don't see how that would differ? The question says "when the rocket's height is 80 feet above ground" which means that h(t)=80 (right?).
Also, how is it possible that, as time passes, the rocket is getting increasingly closer to the ground? I think that's where I get lost...

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Re: A model rocket takes off from an elevated launch pad which is 32 feet  [#permalink]

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02 Jul 2020, 03:36
WBogey
yes you are right rocket will be exactly 80 feet at 3 which is what the question has asked...
I actually misread the question >80 feet..

WBogey wrote:
Archit3110 wrote:
v12345

what you have determined is the value when height is 80 feet , where question has asked ; At which of the following times, in seconds, is the rocket’s height 80 feet above ground?

Only option A; is valid where H = 92 feet

v12345 wrote:
Bunuel wrote:
A model rocket takes off from an elevated launch pad which is 32 feet above the ground. The rocket’s elevation is given by the function $$h(t) = −16t^2 + 64t + 32$$, where $$h(t)$$ represents the height, in feet above ground, after t seconds. At which of the following times, in seconds, is the rocket’s height 80 feet above ground?

I. 2.5
II. 3
III. 4

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

Given,
$$h(t) = −16t^2 + 64t + 32$$
=> $$−16t^2 + 64t + 32 = 80$$
=> $$−16t^2 + 64t - 48 = 0$$
Dividing the equation by (-16), we get
=> $$t^2 - 4t + 3 = 0$$
=> $$(t - 3)(t - 1) = 0$$
=> $$t = 3 or 1$$

Only II. has required value.
Thus, OA is (B).

Hi Archit3110,
Could you please explain the difference, because I don't see how that would differ? The question says "when the rocket's height is 80 feet above ground" which means that h(t)=80 (right?).
Also, how is it possible that, as time passes, the rocket is getting increasingly closer to the ground? I think that's where I get lost...

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Location: India
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A model rocket takes off from an elevated launch pad which is 32 feet  [#permalink]

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02 Jul 2020, 05:17
1
Bunuel wrote:
A model rocket takes off from an elevated launch pad which is 32 feet above the ground. The rocket’s elevation is given by the function $$h(t) = −16t^2 + 64t + 32$$, where $$h(t)$$ represents the height, in feet above ground, after t seconds. At which of the following times, in seconds, is the rocket’s height 80 feet above ground?

I. 2.5
II. 3
III. 4

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

Hello guys!
Here, one can consider plugging in the options if you don't wanna go fighting with the equation! XD

Plugging in II) 3.
h(t)= -16t^2+64t+32
= -16(3)^2 + 64 (3) + 32
= -16 x 9 + 192 + 32
= -144 + 192 + 32
= 48 + 32
= 80

This accurately leads us to get the Height correct.

Hope this helps you buddy! WBogey

IMO,
Option B is the winner, for having II)

Thank you!

Regards,
Raunak Damle
Intern
Joined: 04 May 2020
Posts: 41
Re: A model rocket takes off from an elevated launch pad which is 32 feet  [#permalink]

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02 Jul 2020, 07:49
Bunuel wrote:
A model rocket takes off from an elevated launch pad which is 32 feet above the ground. The rocket’s elevation is given by the function $$h(t) = −16t^2 + 64t + 32$$, where $$h(t)$$ represents the height, in feet above ground, after t seconds. At which of the following times, in seconds, is the rocket’s height 80 feet above ground?

I. 2.5
II. 3
III. 4

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

If t=3:

h(t)=-16t^2+64t+32
=-16(3^2)+64(3)+32
=-16x9+192+32
=-144+192+32
=48+32
=80

Re: A model rocket takes off from an elevated launch pad which is 32 feet   [#permalink] 02 Jul 2020, 07:49