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The velocity, V feet per second, of a model rocket t seconds after 04 Aug 2023, 10:00
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The velocity, V feet per second, of a model rocket t seconds after launch is given by V = -32t + C, where C is a positive constant. What is the velocity of the rocket 2 seconds after it was launched?

(1) The rocket reaches its maximum height and begins descending 1.5 seconds after it was launched.
(2) The rocket's initial velocity was 48 feet per second.
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D
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The velocity, V feet per second, of a model rocket t seconds after 04 Aug 2023, 10:52
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Bunuel
The velocity, V feet per second, of a model rocket t seconds after launch is given by V = -32t + C, where C is a positive constant. What is the velocity of the rocket 2 seconds after it was launched?

(1) The rocket reaches its maximum height and begins descending 1.5 seconds after it was launched.
(2) The rocket's initial velocity was 48 feet per second.
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Formula Given: V = -32t + C ; C is a positive number

Question: V at time = 2 seconds?

Inference: If we can find the value of C, we will be able to answer the question.

Statement 1

(1) The rocket reaches its maximum height and begins descending 1.5 seconds after it was launched.

At its maximum height, the velocity of the rocket is zero. Hence, we know that at t = 1.5, V = 0

0 = -32(1.5) + C

We can find the value of C. The statement alone is sufficient to answer the question. We can eliminate B, C, and E.

Statement 2

(2) The rocket's initial velocity was 48 feet per second.

At t = 0, V = 48

48 = -32(0) + C

C = 48

As we have the value of C, the statement alone is sufficient to answer the question.

Option D
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The velocity, V feet per second, of a model rocket t seconds after 06 Sep 2023, 18:13
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Bunuel
The velocity, V feet per second, of a model rocket t seconds after launch is given by V = -32t + C, where C is a positive constant. What is the velocity of the rocket 2 seconds after it was launched?

(1) The rocket reaches its maximum height and begins descending 1.5 seconds after it was launched.
(2) The rocket's initial velocity was 48 feet per second.
Show more

We need to answer the question:

V = -32(2) + C = ? => C = ?

Statement One Alone:

=> The rocket reaches its maximum height and begins descending 1.5 seconds after it was launched.

According to the given velocity formula, the velocity decreases as time passes after launch. As long as its speed is positive, the rocket can continue to ascend. Once its velocity becomes zero, the rocket will reach its maximum height. So, we have:

-32(1.5) + C = 0

C = 48

Since we have a unique answer to the rephrased question, statement one is sufficient. Eliminate answer choices B, C, and E.

Statement Two Alone:

=> The rocket’s initial velocity was 48 feet per second.

Since, at the initial moment of the launch, t = 0, we have:

-32(0) + C = 48

C = 48

Since we have a unique answer to the rephrased question, statement two is sufficient.

Answer: D
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The velocity, V feet per second, of a model rocket t seconds after 29 Nov 2023, 19:17
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I really like this question. However, I would also like to highlight that this may not be very representative of a GMAT question since to understand the significance of statement one, we would need to have a good understanding of the relationship between height/velocity (which arguably is more physics than math).

Let me know if my assessment is accurate/fair.
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The velocity, V feet per second, of a model rocket t seconds after 29 Nov 2023, 23:53
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HSWorNothing
I really like this question. However, I would also like to highlight that this may not be very representative of a GMAT question since to understand the significance of statement one, we would need to have a good understanding of the relationship between height/velocity (which arguably is more physics than math).

Let me know if my assessment is accurate/fair.
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This is a GMAT Prep (Focus) question, so it is as representative of an actual GMAT as it gets. Questions from GMAT Prep were once used in the actual test.
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The velocity, V feet per second, of a model rocket t seconds after 15 Mar 2024, 04:37
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Bunuel
The velocity, V feet per second, of a model rocket t seconds after launch is given by V = -32t + C, where C is a positive constant. What is the velocity of the rocket 2 seconds after it was launched?

(1) The rocket reaches its maximum height and begins descending 1.5 seconds after it was launched.
(2) The rocket's initial velocity was 48 feet per second.
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­Answer: Option D

Please check the Video explanation here



­
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The velocity, V feet per second, of a model rocket t seconds after 08 Jun 2024, 20:56
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Can anyone explain why the velocity is 0 at maximum height? An explanation would be appreciated rather than just stating it without any reasoning behind it. Thank you­
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The velocity, V feet per second, of a model rocket t seconds after Updated on: 06 Jan 2025, 19:56
Originally posted by HarshavardhanR on 08 Jun 2024, 21:47.
Last edited by HarshavardhanR on 06 Jan 2025, 19:56, edited 1 time in total.
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Confide
Can anyone explain why the velocity is 0 at maximum height? An explanation would be appreciated rather than just stating it without any reasoning behind it. Thank you­
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­Perhaps this example will help.

Remember what happens when we throw a ball up in the air.

- Once we throw the ball up, it travels upward with some velocity.
- It reaches a certain maximum height.
- Then, it starts falling i.e., it travels downward with some velocity.

The key point is this: At that exact maximum height, the ball actually pauses for the smallest of split-seconds, and only then moves downwards. In other words, at that exact point of max height, the velocity of the ball is 0.

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The velocity, V feet per second, of a model rocket t seconds after 09 Jul 2024, 12:44
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but it is nowhere stated that the rocket is flying straight up. the rocket could actually be flying in a curve and reaching a maximum height would not necessarily mean that V=0. A bit imprecise, I think.­
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The velocity, V feet per second, of a model rocket t seconds after Updated on: 11 Aug 2025, 20:04
Originally posted by HarshavardhanR on 09 Jul 2024, 21:38.
Last edited by HarshavardhanR on 11 Aug 2025, 20:04, edited 2 times in total.
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SergejK
but it is nowhere stated that the rocket is flying straight up. the rocket could actually be flying in a curve and reaching a maximum height would not necessarily mean that V=0. A bit imprecise, I think.­
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­To be honest, I agree with this take.

- While it may be inferable that we are dealing with vertical movement only, thanks to the given equation (32 ft/s2 is ---> 9.8 m/s2 ---> which is acceleration due to gravity, which only applies vertically downward ---> so, we must be dealing with purely vertical movement basis the equation), to be able to infer this requires some specific science knowledge beyond general knowledge. So, the question should ideally specify vertical movement.

- It may be that the test-maker intent was to consider the general lay-person understanding ("rocket typically goes straight up"). In which case, the velocity is 0 at the point of maximum height.

- of course, if we consider the rocket to move along a curve (projectile motion), at the point of maximum height -
---> Vertical velocity is 0.
---> Horizontal velocity exists (not 0).

So, strictly speaking, overall velocity is not 0. Agreed.

That said, I think the test-maker intent here is upward movement rather than movement along a curve.

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The velocity, V feet per second, of a model rocket t seconds after 31 Mar 2025, 05:20
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(1)
At max hight and start desending, v=0
-> -1.5v + C=0, -> C = 4.5. Sufficient

(2)
C can be calculated. Sufficient.

D


Ps/
I feel so proud that the physics knowledge I learned during my childhood helped me solve this question easily.
It was worth my love for physics!
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The velocity, V feet per second, of a model rocket t seconds after 10 Aug 2025, 22:08
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Hi experts KarishmaB chetan2u MartyMurray GMATCoachBen

I am still not clear, why this (D) would be the answer here? I think (B) should be the answer.

Using my understanding of Physics here:
1. Velocity at the highest point can't necessarily be zero if rocket has both vertical and horizontal velocity. In that case Statement-1 would be Insufficient.
2. "Rocket launched" can also happen in parabolic trajectory apart from vertical pose only. In former case, it will have both horizontal and vertical velocity components. In that case Statement-1 would be Insufficient.

Can you please let me know which part of the question guides us that we have to assume that rocket has vertical velocity only? I think due to this assumption, answer shown is (D).
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The velocity, V feet per second, of a model rocket t seconds after 10 Aug 2025, 22:29
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It is a model rocket so we can pretty much expect it to be basic - start with an initial velocity, go straight up and velocity reduces because of gravity. Finally reaches the top point when velocity becomes 0 and comes back down. The reason 'velocity' is mentioned - because it is negative while coming down as per the equation. No other reason.

agrasan
Hi experts KarishmaB chetan2u MartyMurray GMATCoachBen

I am still not clear, why this (D) would be the answer here? I think (B) should be the answer.

Using my understanding of Physics here:
1. Velocity at the highest point can't necessarily be zero if rocket has both vertical and horizontal velocity. In that case Statement-1 would be Insufficient.
2. "Rocket launched" can also happen in parabolic trajectory apart from vertical pose only. In former case, it will have both horizontal and vertical velocity components. In that case Statement-1 would be Insufficient.

Can you please let me know which part of the question guides us that we have to assume that rocket has vertical velocity only? I think due to this assumption, answer shown is (D).
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The velocity, V feet per second, of a model rocket t seconds after 11 Aug 2025, 01:15
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The clue is in the equation V = −32t + C.
The constant −32 represents acceleration due to gravity in ft/s2, which applies only to vertical motion.
At the highest point, vertical velocity = 0. The negative sign means downward motion by the usual sign convention (up = positive, down = negative).
If horizontal velocity were involved, we’d need separate equations for x- and y-components. Since only one equation is given, the question is about vertical velocity only.
Therefore, Statement (1) is sufficient, and the answer is (D).
agrasan
Hi experts KarishmaB chetan2u MartyMurray GMATCoachBen

I am still not clear, why this (D) would be the answer here? I think (B) should be the answer.

Using my understanding of Physics here:
1. Velocity at the highest point can't necessarily be zero if rocket has both vertical and horizontal velocity. In that case Statement-1 would be Insufficient.
2. "Rocket launched" can also happen in parabolic trajectory apart from vertical pose only. In former case, it will have both horizontal and vertical velocity components. In that case Statement-1 would be Insufficient.

Can you please let me know which part of the question guides us that we have to assume that rocket has vertical velocity only? I think due to this assumption, answer shown is (D).
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The velocity, V feet per second, of a model rocket t seconds after 11 Aug 2025, 03:07
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agrasan
I am still not clear, why this (D) would be the answer here? I think (B) should be the answer.

Using my understanding of Physics here:
1. Velocity at the highest point can't necessarily be zero if rocket has both vertical and horizontal velocity. In that case Statement-1 would be Insufficient.
2. "Rocket launched" can also happen in parabolic trajectory apart from vertical pose only. In former case, it will have both horizontal and vertical velocity components. In that case Statement-1 would be Insufficient.

Can you please let me know which part of the question guides us that we have to assume that rocket has vertical velocity only? I think due to this assumption, answer shown is (D).
Show more
The question defines the velocity for us by saying the following:

The velocity, V feet per second, of a model rocket t seconds after launch is given by V = -32t + C, where C is a positive constant.

We see that, as defined by the question, the velocity of the rocket has only a vertical component. So, we need to be concerned with the vertical velocity only.
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The velocity, V feet per second, of a model rocket t seconds after 11 Aug 2025, 03:11
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Thanks MartyMurray
Did you identify that questions asks for vertical velocity only due to the co-efficient -32 which can be due to gravity and other frictional forces?
MartyMurray
agrasan
I am still not clear, why this (D) would be the answer here? I think (B) should be the answer.

Using my understanding of Physics here:
1. Velocity at the highest point can't necessarily be zero if rocket has both vertical and horizontal velocity. In that case Statement-1 would be Insufficient.
2. "Rocket launched" can also happen in parabolic trajectory apart from vertical pose only. In former case, it will have both horizontal and vertical velocity components. In that case Statement-1 would be Insufficient.

Can you please let me know which part of the question guides us that we have to assume that rocket has vertical velocity only? I think due to this assumption, answer shown is (D).
The question defines the velocity for us by saying the following:

The velocity, V feet per second, of a model rocket t seconds after launch is given by V = -32t + C, where C is a positive constant.

We see that, as defined by the question, the velocity of the rocket has only a vertical component. So, we need to be concerned with the vertical velocity only.
Show more
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The velocity, V feet per second, of a model rocket t seconds after 11 Aug 2025, 03:31
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Thanks MartyMurray
Did you identify that questions asks for vertical velocity only due to the co-efficient -32 which can be due to gravity and other frictional forces?
MartyMurray
agrasan
I am still not clear, why this (D) would be the answer here? I think (B) should be the answer.

Using my understanding of Physics here:
1. Velocity at the highest point can't necessarily be zero if rocket has both vertical and horizontal velocity. In that case Statement-1 would be Insufficient.
2. "Rocket launched" can also happen in parabolic trajectory apart from vertical pose only. In former case, it will have both horizontal and vertical velocity components. In that case Statement-1 would be Insufficient.

Can you please let me know which part of the question guides us that we have to assume that rocket has vertical velocity only? I think due to this assumption, answer shown is (D).
The question defines the velocity for us by saying the following:

The velocity, V feet per second, of a model rocket t seconds after launch is given by V = -32t + C, where C is a positive constant.

We see that, as defined by the question, the velocity of the rocket has only a vertical component. So, we need to be concerned with the vertical velocity only.
Show more
Yes, the presence of the single coefficient -32 indicates that only gravity is playing a role. If friction or horizontal velocity were taken into consideration, a more complex formula would be required for representing the trajectory of the rocket.

That said, I don't find this question to be a fair question because answering it correctly basically requires prior understanding of everything we're talking about, which is not what the GMAT is meant to test.
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The velocity, V feet per second, of a model rocket t seconds after 21 Sep 2025, 11:20
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I do not understand why would we take v=0?

RishiAgarwal231
statement 1: assume v=0 (before it begins declining, it stops hence v=0) in the equation and t=1.5 and you will get C as 48. Now for 2 secs later, speed is 2*-32 + 48. (Sufficient)

statement 2: Assume v=48 in the equation and t=0 (initial time is 0), you will get C as 48. Again for 2 secs later it is 2*-32 + 48. (Sufficient)

Overall Answer: D (each alone is sufficient)
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The velocity, V feet per second, of a model rocket t seconds after 21 Sep 2025, 11:49
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nandini14
I do not understand why would we take v=0?


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When the rocket goes up, it keeps slowing down until it reaches the very top, its maximum height. At that exact moment, it is not moving upward anymore, and it has not yet started moving downward. For that instant, its velocity is zero. That’s why in statement (1) we put v = 0 at t = 1.5 seconds.
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