# Projectile motion of a fired gun

#### 1MileCrash

1. Homework Statement

A projectile is fired horizontally from a gun that is 99.0 m above flat ground, emerging from the gun at a speed of 250 m/s

how long is it in the air?

how far does it travel horizontally?

vertical component of velocity as it strikes the ground?

2. Homework Equations

3. The Attempt at a Solution

To find how long it is in the air for, I built a y position function:

y = 99 + -4.9t^2

And solved for when y = 0 to get a t of 4.49 seconds.

To find how far it traveled horizontally, I built an x position function:

x = 250t

And solved for when t = 4.49 seconds to get 1122.5 meters traveled horizontally.

For the vertical component of velocity as it strikes the ground, I simply differentiated my y position formula and solved for t = 4.49 seconds, but this is incorrect. I'm not sure I fully understand what the "vertical component of velocity" is.

Thanks.

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#### S_Happens

Gold Member
So, why do you say it's incorrect? What answer did you get for that part and what "correct" answer are you comparing it to?

The vertical component is your y component, just like you thought.

#### 1MileCrash

Sorry, my first two answers are correct. My last is incorrect, which is -44.

EDIT: It just needed to be positive, it's a magnitude.

#### 1MileCrash

Not worth making a new topic over:

Identical guns fire identical bullets horizontally at the same speed from the same height above level planes, one on the Earth and one on the Moon. Which of the following three statements is/are true?

The horizontal distance covered on the moon is greater
The flight time is less for the bullet on earth
The velocity is same at the point of impact

First two?

#### lewando

Homework Helper
Gold Member
First two?
If you understand the concepts, then you should have no doubts about your answer. Do you have any doubts about the true/false nature of a specific statement?

#### 1MileCrash

I have doubts that they are talking about the magnitude of the velocity vector vs horizontal component alone in the last.

#### lewando

Homework Helper
Gold Member
I read "velocity at point of impact" as the composite velocity.

#### S_Happens

Gold Member
I have doubts that they are talking about the magnitude of the velocity vector vs horizontal component alone in the last.
Yes, it's asking about a composite velocity, but if you break down the components it becomes quite simple. If you can answer the following two questions without doing the math, then you understand the concepts. If not, then do the math and it should become clear.

How do the x component velocities compare (is one larger or are they equivalent)?

How do the y component velocities compare?

#### 1MileCrash

Of course it is quite clear assuming on or the other is the question intent. Same horizontal, different vertical, therefore different total.

#### Coaster_Man

Not worth making a new topic over:

Identical guns fire identical bullets horizontally at the same speed from the same height above level planes, one on the Earth and one on the Moon. Which of the following three statements is/are true?

The horizontal distance covered on the moon is greater
The flight time is less for the bullet on earth
The velocity is same at the point of impact

First two?
Just think of how the different gravities affect the bullets and other forces such as friction in the air and your answer should be quite simple to come to.

#### 1MileCrash

Again, my doubt lies within the way the question is worded.

#### lewando

Homework Helper
Gold Member
It is natural to have doubt's based on exposure to poorly-worded questions, typos, omissions, bad translations, etc.

But in this case, the question is not poorly worded. "velocity" simply means composite velocity. If you look back at the OP question, they took the time to explicitly write "vertical component of velocity" when they meant vertical component of velocity.

If you still have a doubt, answer the question, but stipulate your interpretation of the word "velocity" and answer appropriately.

Best regards.

#### S_Happens

Gold Member
Of course it is quite clear assuming on or the other is the question intent. Same horizontal, different vertical, therefore different total.
My two questions were for conception/understanding. They weren't actually in reference to solving the original question. Answering those two questions helps to highlight the differences.

It is quite clear that the 2nd original question ("which of these is true") is asking for the actual velocity of the projectile(s), not simply one or another component.

#### 1MileCrash

Alright, thanks guys.