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When an object is dropped from a building, its height above the ground

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When an object is dropped from a building, its height above the ground  [#permalink]

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New post 18 Aug 2018, 08:00
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A
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Difficulty:

  25% (medium)

Question Stats:

76% (01:47) correct 24% (02:03) wrong based on 33 sessions

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When an object is dropped from a building, its height above the ground is given by the formula h = y – gt^2 where y is the height of the building in meters, g is a constant, and t is the time in seconds since the object was dropped. What is the height of an object dropped from a 100 meter tall building 2 seconds after being dropped?

(1) An object is 74 meters above the ground 2 seconds after being dropped from a building that is z meters tall.

(2) The height of an object dropped from a 150 meter tall building is 61.2 meters 3 seconds after being dropped.

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Re: When an object is dropped from a building, its height above the ground  [#permalink]

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New post 18 Aug 2018, 08:01
dabaobao wrote:
When an object is dropped from a building, its height above the ground is given by the formula h = y – gt^2 where y is the height of the building in meters, g is a constant, and t is the time in seconds since the object was dropped. What is the height of an object dropped from a 100 meter tall building 2 seconds after being dropped?

(1) An object is 74 meters above the ground 2 seconds after being dropped from a building that is z meters tall.

(2) The height of an object dropped from a 150 meter tall building is 61.2 meters 3 seconds after being dropped.



Official Solution (Credit: Manhattan Prep)



This question contains a Formula. Jot down that formula and any notes needed to keep the variables straight.

h = y – gt^2

y = building height, g = constant, t = time

The question asks about the height of an object in a particular set of circumstances. Fill in the information about this case into the formula.

h = 100 – g(2^2)

h = 100 – 4g

What information do you need to solve for the height h? The value of the constant g: if you knew g, you could plug it into the equation above to solve for h. So the question can be Rephrased as:

What is g?


(1) INSUFFICIENT: Plug the information from the statement into the formula.

74 = z – g(2^2)

74 = z – 4g

Can you solve for g? You can’t. You could rearrange the equation to isolate g, but there is still another variable in the equation.

g=(z−74)/4

This statement is not sufficient. Eliminate choices (A) and (D).


(2) SUFFICIENT: Plug the information from the statement into the formula.

61.2 = 150 – g(3^2)

61.2 = 150 – 9g

In this case, you can solve for g because it is the only variable in the equation. Since this is a data sufficiency problem, you don’t have to go through the exact calculations. This statement is sufficient. Eliminate choices (C) and (E).

The correct answer is (B).
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Re: When an object is dropped from a building, its height above the ground  [#permalink]

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New post 18 Aug 2018, 11:51
dabaobao wrote:
When an object is dropped from a building, its height above the ground is given by the formula h = y – gt^2 where y is the height of the building in meters, g is a constant, and t is the time in seconds since the object was dropped. What is the height of an object dropped from a 100 meter tall building 2 seconds after being dropped?

(1) An object is 74 meters above the ground 2 seconds after being dropped from a building that is z meters tall.

(2) The height of an object dropped from a 150 meter tall building is 61.2 meters 3 seconds after being dropped.



St 1: WE can form an equation in the tune of 74 = z-gt^2 - insufficient
St 2: This forms a detailed equation that will help you find g and subsequently answer the question - sufficient

Note: I do not generally solve the DS sums for answers to save time. Please excuse the brevity in this response.
Re: When an object is dropped from a building, its height above the ground &nbs [#permalink] 18 Aug 2018, 11:51
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