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Math Expert V
Joined: 02 Sep 2009
Posts: 61385
The maximum height reached by an object thrown directly upward is dire  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 75% (01:58) correct 25% (02:19) wrong based on 173 sessions

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The maximum height reached by an object thrown directly upward is directly proportional to the square of the velocity with which the object is thrown. If an object thrown upward at 16 feet per second reaches a maximum height of 4 feet, with what velocity must the object be thrown upward to reach a maximum height of 9 feet?

A. 12 feet per second
B. 16 feet per second
C. 18 feet per second
D. 24 feet per second
E. 48 feet per second

Kudos for a correct solution.

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Re: The maximum height reached by an object thrown directly upward is dire  [#permalink]

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Is the answer D? Given that the Height is directly proportional to the square of the velocity, I created the following equation, plugged in the values and solved.

H1/(V1)^2 = H2/(V2)^2  Intern  Joined: 28 Jan 2013
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The maximum height reached by an object thrown directly upward is directly proportional to the square of the velocity with which the object is thrown. If an object thrown upward at 16 feet per second reaches a maximum height of 4 feet, with what speed must the object be thrown upward to reach a maximum height of 9 feet?

height(h) is directly proportional to square of the velocity(v).
h directly proportional to $$v^2$$
h=k$$v^2$$ where k is a constant
$$\frac{h}{v^2}$$ = k
from the above, we can derive below equations
$$\frac{h1}{(v1)^2}$$= $$\frac{h2}{(v2)^2}$$

Substituting the values (h1=4,v1=16,h2=9)
$$\frac{4}{16^2}$$ = $$\frac{9}{(v2)^2}$$
v2=24 feet per second

Ans:D
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Re: The maximum height reached by an object thrown directly upward is dire  [#permalink]

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Bunuel wrote:
The maximum height reached by an object thrown directly upward is directly proportional to the square of the velocity with which the object is thrown. If an object thrown upward at 16 feet per second reaches a maximum height of 4 feet, with what speed must the object be thrown upward to reach a maximum height of 9 feet?

A. 12 feet per second
B. 16 feet per second
C. 18 feet per second
D. 24 feet per second
E. 48 feet per second

Kudos for a correct solution.

v^2 is directly proportional to max height
16^2 is directly proportional to 4
256 is directly proportional to 4 >>> 256 / 4 = 64 >>> Now we are looking for max height of 9 >>> 9*64 = 576

(24^2 = 576)

Therefore 24^2 is directly proportional to max height of 9

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Re: The maximum height reached by an object thrown directly upward is dire  [#permalink]

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As per given information assume h1 = max height of object at first throw, v1=velocity of the object on first throw; h2 = max height of object at second throw, v2=velocity of the object on second throw
H is proportional to velocity ^2 =>
h1/h2= (v1/v2)^2 => 4/9= (16/x)^2 => 2/3=16/x => x=24

Thanks,
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Height is proportional to the square of velocity

h = k * v^2 (k is the constant)

4 = k * 16 ^ 2

or, k = 4 / 16 ^2

now question asking what will be speed required to attain 9 feet

9 = 4/16^2 * v^2 (Putting the value of K)

or v^2 = 9 * 16^2 / 4

v = 3*16/2 (taking under root both sides)

v = 24 feet / sec Joined: 24 Oct 2012
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Re: The maximum height reached by an object thrown directly upward is dire  [#permalink]

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Bunuel wrote:
The maximum height reached by an object thrown directly upward is directly proportional to the square of the velocity with which the object is thrown. If an object thrown upward at 16 feet per second reaches a maximum height of 4 feet, with what speed must the object be thrown upward to reach a maximum height of 9 feet?

A. 12 feet per second
B. 16 feet per second
C. 18 feet per second
D. 24 feet per second
E. 48 feet per second

Kudos for a correct solution.

Height is directly proportional to square of Velocity

H1 / H2 = (V1)^2 / (V2)^2

4/9 = 16^2 / x^2

Solving we get x = 24

Option D
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Re: The maximum height reached by an object thrown directly upward is dire  [#permalink]

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Bunuel wrote:
The maximum height reached by an object thrown directly upward is directly proportional to the square of the velocity with which the object is thrown. If an object thrown upward at 16 feet per second reaches a maximum height of 4 feet, with what speed must the object be thrown upward to reach a maximum height of 9 feet?

A. 12 feet per second
B. 16 feet per second
C. 18 feet per second
D. 24 feet per second
E. 48 feet per second

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

Typically with direct proportion problems, you will be given “before” and “after” values. Simply set up ratios to solve the problem. For example, $$\frac{y_1}{x_1}$$ can be used for the “before” values and , $$\frac{y_2}{x_2}$$ can be used for the “after” values. You then write, $$\frac{y_1}{x_1}=\frac{y_2}{x_2}$$, since both ratios are equal to the same constant k. Finally, you solve for the unknowns.

In the problem given above, be sure to note that the direct proportion is between the height and the square of the velocity, not the velocity itself. Therefore, write the proportion as $$\frac{h_1}{(v_1)^2}=\frac{h_2}{(v_2)^2}$$. Substitute the known values h1 = 4, v1 = 16, and h2 = 9:

$$\frac{4}{(16)^2}=\frac{9}{(v_2)^2}$$

$$v_2=24$$.

The object must be thrown upward at 24 feet per second.

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Re: The maximum height reached by an object thrown directly upward is dire  [#permalink]

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The maximum height reached by an object thrown directly upward is directly proportional to the square of the velocity with which the object is thrown. If an object thrown upward at 16 feet per second reaches a maximum height of 4 feet, with what speed must the object be thrown upward to reach a maximum height of 9 feet?
h = height, x = constant of proportionality, v = velocity
First solve for the constant. xh=v^2. x(4)=16^2 => x = 64
Second solve for v. 64(9)=v^2

A. 12 feet per second
B. 16 feet per second
C. 18 feet per second
D. 24 feet per second
E. 48 feet per second
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Re: The maximum height reached by an object thrown directly upward is dire  [#permalink]

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Unitary method for directly/indirectly proportional problems:

Theory:
Let the max. height reached by the object be $$h$$. Let the velocity with which the object is thrown be $$v$$.
Given, $$h-->v^2$$.

Now, hmax= 4 when the object is thrown at the speed (velocity of the object) of $$16 ft/sec$$.
For $$h = 9$$ the $$speed$$ $$v^2 = ?$$

$$\frac{16*16*9}{4} = v^2$$

Ans: 24 - D

Originally posted by PratikHP on 14 Aug 2015, 10:34.
Last edited by PratikHP on 21 Aug 2015, 10:18, edited 3 times in total.
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Re: The maximum height reached by an object thrown directly upward is dire  [#permalink]

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Bunuel wrote:
The maximum height reached by an object thrown directly upward is directly proportional to the square of the velocity with which the object is thrown. If an object thrown upward at 16 feet per second reaches a maximum height of 4 feet, with what speed must the object be thrown upward to reach a maximum height of 9 feet?

A. 12 feet per second
B. 16 feet per second
C. 18 feet per second
D. 24 feet per second
E. 48 feet per second

Kudos for a correct solution.

h =k*(v^2)
4=k*(16^2)
k=1/64
9=(v^2)*(1/64)
v^2 = 9*64
v=3*8=24
Hence, the correct option is D
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Re: The maximum height reached by an object thrown directly upward is dire  [#permalink]

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i got to the answer choice by approximations
4 ft upwards = k * 16^2 or 256k = 4, out of which we can see that k is 1/64
now we have another equation:
9 ft = k * x (velocity)
or 9 = x/64
x = 9*64 that is ~600. Which value of an integer is closer to this number? well, 25 squared is 625. It must be smth 20+ but less than 25
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The maximum height reached by an object thrown directly upward is dire  [#permalink]

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Isn't the question ambiguous? Because it derives a corelation between height and velocity and asks us about the speed. We all know that speed and velocity are totally different terms.Am I correct? Bunuel please help ..

Originally posted by sahilsnpt on 07 Mar 2018, 00:51.
Last edited by sahilsnpt on 07 Mar 2018, 01:13, edited 1 time in total.
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Re: The maximum height reached by an object thrown directly upward is dire  [#permalink]

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sahilsnpt wrote:
Isn't the question ambiguous? Because derives a corelation between height and velocity and asks us about the speed. We all know that speed and velocity are totally different terms.Am I correct? Bunuel please help ..

Hey sahilsnpt ,

Lol, I could see you are a Physics student.  Yeah, it should be velocity. I have modified the original question.

Thank you!
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