Projectile motion of a fired gun

In summary, the bullets fired from the guns on the Earth and Moon have the same velocity at the point of impact, but the bullets on the Earth travel a longer distance.
  • #1
1MileCrash
1,342
41

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?

Homework Equations





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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  • #2
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.
 
  • #3
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.
 
  • #4
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?
 
  • #5
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?
 
  • #6
I have doubts that they are talking about the magnitude of the velocity vector vs horizontal component alone in the last.
 
  • #7
I read "velocity at point of impact" as the composite velocity.
 
  • #8
1MileCrash said:
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?
 
  • #9
Of course it is quite clear assuming on or the other is the question intent. Same horizontal, different vertical, therefore different total.
 
  • #10
1MileCrash said:
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.
 
  • #11
Again, my doubt lies within the way the question is worded.
 
  • #12
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.
 
  • #13
1MileCrash said:
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.
 
  • #14
Alright, thanks guys.
 

1. What is projectile motion?

Projectile motion is the motion of an object that is launched into the air and then moves under the influence of gravity alone. It follows a curved path known as a parabola.

2. How does a fired gun exhibit projectile motion?

A fired gun exhibits projectile motion because the bullet is initially launched with a high velocity and then moves under the influence of gravity, following a curved path until it hits a target or falls to the ground.

3. What factors affect the projectile motion of a fired gun?

The factors that affect the projectile motion of a fired gun include the initial velocity of the bullet, the angle at which the gun is fired, the mass of the bullet, and the force of gravity.

4. How can we calculate the range of a fired gun?

The range of a fired gun can be calculated using the formula R = (v^2/g) * sin(2θ), where R is the range, v is the initial velocity, g is the acceleration due to gravity, and θ is the angle of elevation.

5. Is the trajectory of a fired gun affected by air resistance?

Yes, air resistance can affect the trajectory of a fired gun. As the bullet travels through the air, it experiences air resistance which can cause it to deviate from its expected path. This is why long-range snipers must take into account air resistance when aiming their shots.

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