What is the velocity of a dart that is fired?

[DeathEater]

Homework Statement

a hunter is trying to kill an armadillo that is 70 m away. To kill it, the hunter fires a dart at an angle 30 degrees above the horizontal. What must be the velocity of the dart in order to hit the armadillo?

Homework Equations

Vx=Vcosθ
Vy=Vsinθ
Δx= (Vix)(time)+½(acceleration)(time)²

The Attempt at a Solution

I assume that this will take on a shape of basically two right triangles back to back, since that will mimic the shape of the parabola the projectile makes. I broke the angle into components (only for one of the right triangles, and to find the distance traveled in the y direction and the hypotenuse, which is the dart basically) and I got that the hypotenuse is cos (30)= 35/ hypotenuse (I used 35 since it is only one of the triangles, so the base is half the distance traveled in the x direction). After solving I got the hypotenuse = 40.4145 m and using the same method and Tangent, got that the y-component is 20.207 m for one of the triangles.

I do not really know where to go after breaking it into components though, and if I made mistakes above, I would like to know so that I may correct and try to understand better

 

[Simon Bridge]

Bad approach... do not approximate a parabola by two triangles... its way way off.
Note: you do not need the tangent or the hypotenuse to get components...
It looks like you need to reread your course notes.

Try using kinematics or Newton's laws instead.
Velocity-time graphs can help a lot here: you will wantbto bresk the initual velocity into components.

 

[Mister T]

Homework Equations

Vx=Vcosθ
Vy=Vsinθ
Δx= (Vix)(time)+½(acceleration)(time)²

Because the acceleration in the x-direction is zero, this last equation should instead be

$\Delta x=(v_{ix})(\mathrm {time})$

But you will need an additional equation that includes $v_{iy}$ and involves the acceleration in the y-direction.

 

[DeathEater]

Bad approach... do not approximate a parabola by two triangles... its way way off.
Note: you do not need the tangent or the hypotenuse to get components...
It looks like you need to reread your course notes.

Try using kinematics or Newton's laws instead.
Velocity-time graphs can help a lot here: you will wantbto bresk the initual velocity into components.

my teacher has not taught this before, we have always had a given velocity, so it was very confusing when there wasn't one. And my teacher was the one who drew the triangle... I really do not know what to do. I am appreciative of all help and I really want to understand this.

 

[Mister T]

Well, you can draw triangles to illustrate $\vec{v}$ and it's components, but not to approximate the the shape of the projectile's path.

Do you have a textbook for this course? Try looking up "range of a projectile".

 

[DeathEater]

Well, you can draw triangles to illustrate $\vec{v}$ and it's components, but not to approximate the the shape of the projectile's path.

Do you have a textbook for this course? Try looking up "range of a projectile".

this question was on a previous test. He didn't explain it, and the things we learned prior to taking the test was kinematic equations and how to use SOHCAHTOA to break things into components. Using that knowledge only (and no we do not have a textbook) how could I solve this? I know that the point of these forums is to try to prick and prod until I come up with the discovery on my own, but I really have absolutely no idea what to do. We haven't discussed Newtons laws or anything either

 

[Mister T]

You need to take each kinematic equation for one-dimensional motion and turn it into a pair of equations, one for the horizontal component of the motion and one for the vertical component.

I suggest a trip to the library or bookstore to find an introductory physics textbook.

See Post #3.

 

[DeathEater]

You need to take each kinematic equation for one-dimensional motion and turn it into a pair of equations, one for the horizontal component of the motion and one for the vertical component.

I suggest a trip to the library or bookstore to find an introductory physics textbook.

See Post #3.

well how would I be able to use the equations together to find it?

 

[Mister T]

well how would I be able to use the equations together to find it?

The are connected by the time t. The time it takes for the horizontal position to change equals the time it takes for the vertical position to change.

 

[DeathEater]

The are connected by the time t. The time it takes for the horizontal position to change equals the time it takes for the vertical position to change.

so I use 70 m for the x, and then using the angle and x do I find the y component which is 20.207 m?(I think)

 

[Mister T]

$\Delta x=70 \ \mathrm{m}$, that was given.

But $\Delta y \neq 20.207 \ \mathrm{m}$ as we've already told you.

Your only option, other than ignoring our advice, is to follow it.

 

[DeathEater]

$\Delta x=70 \mathrm{m}$, that was given.

But $\Delta y \neq 20.207 \mathrm{m}$ as we've already told you.

Your only option, other than ignoring our advice, is to follow it.

I do not know how to go about solving it and how to find the change in y as I have already said many times before.

 

[Mister T]

We know. Sorry, but if you're not willing to follow our instructions there's no way we can help you learn.

 

[DeathEater]

We know. Sorry, but if you're not willing to follow our instructions there's no way we can help you learn.

I am following the instructions, you are just assuming that I know how to do things that I do not and have not been taught

 

[Mister T]

I am following the instructions, you are just assuming that I know how to do things that I do not and have not been taught

You've been to the library or bookstore, picked up an introductory physics textbook, taken each one-dimensional kinematics equation and turned it into a pair of equations, and looked up "range of a projectile"?

I'm not assuming you know how to do each of those things. I am assuming you can do the first two. And I'm hoping you can learn the others. Because I know that if you get stuck along the way we are here to help you.

 

[DeathEater]

You've been to the library or bookstore, picked up an introductory physics textbook, taken each one-dimensional kinematics equation and turned it into a pair of equations, and looked up "range of a projectile"?

I'm not assuming you know how to do each of those things. I am assuming you can do the first two. And I'm hoping you can learn the others. Because I know that if you get stuck along the way we are here to help you.

well I did look up range of a projectile and got the equation

. The only problem is that if I am doing this for X, then acceleration from gravity (g) would be zero...

 

[Simon Bridge]

... back up.
Is this part of a physics course?
Have you completed prior material on kinematics?
Have you completed prior material on Newton's laws of motion?
Have you completed prior material on vectors?

... without these topics, you cannot complete the assignment.
Physics courses always complete these topics before starting on projectile motion, which is why knowledge of these topics is being assumed. If you do not have knowledge of these topics, you will have to go back over your course and back tgrough your textbook and notes to gain the needed knowledge. We cannot just give you physics lessons here.

 

[Simon Bridge]

Note... g appears in the equation for range because $v_0$ is the magnitude of the initial velocity not just the horizontal velocity. You need both horizontal and vertical components to complete the assignment because gravity affects the motion of the dart... so gravity will appear in its equations of motion.

You can use the equation to complete the assignment, but you won't understand it.

 

[DeathEater]

... back up.
Is this part of a physics course?
Have you completed prior material on kinematics?
Have you completed prior material on Newton's laws of motion?
Have you completed prior material on vectors?

... without these topics, you cannot complete the assignment.
Physics courses always complete these topics before starting on projectile motion, which is why knowledge of these topics is being assumed. If you do not have knowledge of these topics, you will have to go back over your course and back tgrough your textbook and notes to gain the needed knowledge. We cannot just give you physics lessons here.

yes, it is part of a physics course, no we have not learned about the laws of Newton, and no we do not have a textbook and the notes are minimal. This problem was on a previous test of mine, so my teacher assumed that I should know how to do this, which I don't.

 

[DeathEater]

Note... g appears in the equation for range because $v_0$ is the magnitude of the initial velocity not just the horizontal velocity. You need both horizontal and vertical components to complete the assignment because gravity affects the motion of the dart... so gravity will appear in its equations of motion.

You can use the equation to complete the assignment, but you won't understand it.

using the equation though, would it be 70= ((vo²)/ 9.81)* sin (2*30) ----> 70 /sin(60)= (vo²)/9.81 ----> 80.83= (vo²)/ 9.81 -----> 80.83*9.81= vo² ----> 792.12=vo²------> vo =28 m/s (after finding the square root)

 

[Mister T]

well I did look up range of a projectile and got the equation

. The only problem is that if I am doing this for X, then acceleration from gravity (g) would be zero...

Where did you look this up? Textbooks and other sources explain this. The equation for the horizontal displacement is combined with the equation for the vertical displacement to eliminate the time t. The resulting equation includes the magnitudes of both the horizontal displacement R and the vertical acceleration g.

 

[Mister T]

------> vo=28 m/s

Check your answer using the scheme we discussed in Post #3.

Then do the same for the equation for the vertical displacement.

Find the time of flight.

 

[Simon Bridge]

You never learned F=ma ? Really?
You have a lot of work to do... you can google the topic that you do not know in order to find learning materials online.
Also try to source a secondary school level physics textbook.

Why would your teacher assume you could do the problem without having covered the knowledge? That is nonsense: you are describing an incompetent teacher and you won't be the only one to be struggling. Do others in your class have the same trouble?

What information had you covered? If we do not know where you were supposed to start from, we cannot really help you.

Note: I don't check people's arithmetic.

 

[Mister T]

It's pretty common to cover projectile motion before covering introductory dynamics and Newton's Laws. It looks to me like the teacher is just transitioning between one-dimensional kinematics and projectile motion. Either the teacher gave the students a problem that was over their heads, or the student failed to grasp the teacher's introductory remarks on the topic.

In my experience the secondary school textbooks are horrible. A motivated high school student would be much better off with a freshman-level algebra-based textbook, in my opinion.

 

[Simon Bridge]

Common where?

We'd need at least kinematics and basic vectors... but that's a geometry course rather than a physics one.
Of course anything can be taught by rote, "these are the ballistics equations"...

 

[Mister T]

The vast majority of college-level introductory physics textbooks do it that way. One used to see a delay in the presentation of projectiles until after dynamics and Newton's Laws in at least a substantial minority, but not so for at least the last 10 years, maybe 20 or more.

Note that position, velocity, and acceleration vectors, along with a formal mathematical treatment of their properties, can be introduced with no reference to forces or force vectors. As I said, this is common.

I do remember, though, the debates over the shortcomings of doing it this way. Similar to teh debates over whether vectors should be introduced before or after one-dimensional kinematics. Usually it's after, but there are some very good books out there that do it before.

 

[Simon Bridge]

Admittedly I have not seen recent college texts... NZ secondary school takes an experimental approach to physics.

 

[Mister T]

Ahhh, then I should clarify. American secondary high school textbooks are crap. The politicians have become so involved in their selection that they are of little use.

Read Feynman's account of his involvement in Surely Your Joking, Mr. Feynman. Very entertaining book for many reasons.

I found this account here: http://www.textbookleague.org/103feyn.htm

 

[DeathEater]

well I didn't fail to grasp the teachers intro remarks, I write everything. And on a side note, the test has long passed, and the teacher refused to work the problems to show us how to do it. I honestly just want to know the full process, and I am not gaining any better understanding of this problem whatsoever from reading what you have written, as my actual knowledge differs from what I think you assume I know.

 

[Mister T]

well I didn't fail to grasp the teachers intro remarks, I write everything.

It could be, then, that I'm mistaken. I was just trying to figure out why the teacher would have drawn those triangles. The vertical and horizontal legs could be used to find the vertical and horizontal displacements, but the hypotenuse cannot be used in that same way, or indeed in any meaningful way.

And on a side note, the test has long passed, and the teacher refused to work the problems to show us how to do it. I honestly just want to know the full process, and I am not gaining any better understanding of this problem whatsoever from reading what you have written,

No, there's no way it could. Nobody can gain an understanding of something as complex as projectile motion from an online conversation. It would take me a few hours of instruction to get you started in the process, followed by a few hours of effort on your part.

as my actual knowledge differs from what I think you assume I know.

Nope! That's not the reason. I was doing the best I could under the circumstances. All I can do in this venue is advise and guide, and possibly teach a bit along the way.

Really, though, if you would just pick up an introductory College Physics textbook for a few dollars at a used book store or online, it would cover all of projectile motion thoroughly. In a situation like that it would be possible for you to learn it.