Volcano Question, PHYS 200 final

[David89]

Homework Statement

On my physics 200 final from Athabasca

A volcano shoots off a rock at a 39 degree angle, at an elevation of 1200m, and the rock has a horizontal range of 5500m.

X = 5500m
Y0 = 1200m
Vx = Unknown
Vy = Unknown
V = Unknown
t = Unknown
a (vertical) = g = -9.8 m/s^2

Homework Equations

Equation for horizontal motion: (Vx)(t) = X
Equation for vertical motion: Y = (Y0) + (Vy)(t) +0.5at^2

The Attempt at a Solution

No idea, I don't think there is enough provided information to solve, and this question messed me up on my final pretty bad.

I did end up using the relation V0^2*sin(a)^2 / g, but I know this only works for projectile motion on level ground. I used it anyways cause I didn't know what else to do...

 

[jbriggs444]

Equation for horizontal motion: (Vx)(t) = X
Equation for vertical motion: Y = (Y0) + (Vy)(t) +0.5at^2

You already know the launch angle. Rather than solving for $v_x$ and $v_y$ independently, why not make use of the launch angle and put v into your equations instead. That leaves you with two equations and how many unknowns?

 

[David89]

This would give me
Vx = Vcos39
Then the equation for motion would be Vcos39*t = 5500 (two unknowns, V and t)

Vy = Vsin39
Equation for motion would be Y = 1200 + Vsin39*t + 0.5(-9.8)t^2 (three unknowns, V and t and Y)

This is where I got stuck, I could solve eq. 1 for t or V, and then put into eq. 2, but I would still have two unknowns, the total vertical displacement and whatever variable I did not solve for.

 

[jbriggs444]

This would give me
Vx = Vcos39
Then the equation for motion would be Vcos39*t = 5500 (two unknowns, V and t)

Vy = Vsin39
Equation for motion would be Y = 1200 + Vsin39*t + 0.5(-9.8)t^2 (three unknowns, V and t and Y)

As I read the problem, Y is known. You are expected to assume that the launch point is 1200m above the height of the surrounding plain.

 

[David89]

Yes that is correct. The initial height that the rock is launched from is 1200 m, but the total vertical displacement is not known.

The equation for vertical motion would be Y = 1200 + Vsin39*t + (-9.8)t^2

If I solved for V in the horizontal motion equation, V = 5500/t*cos39, then the vertical equation for motion would be Y = 1200 + 5500tan39/t + (-9.8)t^2

Could you set Y to zero and solve for t?

 

[David89]

If you set Y to zero, you get the time when the rock is 1200 m above ground, traveling some angle and velocity that is unknown.

I don't know...thanks for the back and forth though its helping me a lot

 

[Chestermiller]

No. Y=1200 at t = 0, and Y = 0 when the rock lands.

 

[David89]

Ohhhh, ok, I think I get it, when the vertical displacement is zero, the rock is on the ground.

I was changing the reference frame for some reason, putting Y=0 at 1200m elevation so it looked like the equation in post 6.

If I solve for t, then 0 = 1200 + 5500/t*cos39 -4.9t^2, at this point could I use the quadratic formula?

 

[Chestermiller]

Ohhhh, ok, I think I get it, when the vertical displacement is zero, the rock is on the ground.

I was changing the reference frame for some reason, putting Y=0 at 1200m elevation so it looked like the equation in post 6.

If I solve for t, then 0 = 1200 + 5500/t*cos39 -4.9t^2, at this point could I use the quadratic formula?

Why is there a t in the denominator, and what happened to the sin 39 in the numerator?

 

[David89]

OHHH, so if I plug in V for the horizontal equation of motion into the vertical equation for motion, 0 = 5500sin39*t/t*cos39 -4.9t^2.

The t's in the first term cancel, and sin39/cos39 is equal to tan39, so our equation becomes 0 = 5500tan39 - 4.9t^2.

OR

-4454 = -4.9t^2

sqrt(-4454/-4.9) = t,

or t = 30.1 seconds.

Is this correct?

 

[Chestermiller]

OHHH, so if I plug in V for the horizontal equation of motion into the vertical equation for motion, 0 = 5500sin39*t/t*cos39 -4.9t^2.

The t's in the first term cancel, and sin39/cos39 is equal to tan39, so our equation becomes 0 = 5500tan39 - 4.9t^2.

OR

-4454 = -4.9t^2

sqrt(-4454/-4.9) = t,

or t = 30.1 seconds.

Is this correct?

No. You need to get the algebra correct.

 

[David89]

Hmmmm ok. I will rewrite this on paper and post back soon

 

[David89]

Ok, I think this is good

 

[Chestermiller]

Ok, I think this is good

Good. Now, for V?

 

[David89]

I solved for Vx, Vy, max height, and final velocity as well.

I really needed to solve this question.

I think it's all good.

 

[jfnn]

That all looks right to me. Excellent!

Congratulations on completing the course--I am also in this course, and I will be done Thursday at noon (write my final exam then). I can't wait.

How did you think it went overall compared to the assignments/practice exams? I found the midterm to be easier than the assignments/practice exams myself :P

Best of luck!

 

[jbriggs444]

The t's in the first term cancel, and sin39/cos39 is equal to tan39, so our equation becomes 0 = 5500tan39 - 4.9t^2.

One thing that can be helpful when doing algebra is to resist putting in numbers until you have a formula for the final answer and are ready to evaluate it. There a few reasons for doing this including:

* If the terms cancel, it is easier to recognize if you have variable names.
* It usually makes the equations less cluttered.
* One is not tempted to combine the constants early and carry huge numbers of insignificant digits through the algebra.
* It is easier for the reader to know what each term means.
* It can make it obvious how the final answer depends on each of the givens of the problem.
* You can leave the units out of the algebra with more confidence, knowing that they are safely stashed away in the variables you are manipulating.

So instead of $5500\ tan 39 - 4.9t^2$ you could write $r\ tan \theta - \frac{1}{2}gt^2$.

Also, posting with embedded LaTeX makes for much more readable formulas.

 

[David89]

That all looks right to me. Excellent!

Congratulations on completing the course--I am also in this course, and I will be done Thursday at noon (write my final exam then). I can't wait.

How did you think it went overall compared to the assignments/practice exams? I found the midterm to be easier than the assignments/practice exams myself :P

Best of luck!

at the risk of making you nervous, I will say that I felt the exam was much harder than the midterms, assignments, and questions on the lab reports. I had 89% in the course going into the exam, and I'm not confident that I got a 65%.

I did all the assigned problems twice, the practice problems, and got an 85% on the practice final (self-assessed).

Variables I could have controlled,
1. My assumed attitude that the problems on the exam were going to be similar to the problems given in the textbook.
The problems on the practice final pull from several chapters at once and you have to utilize the tools learned in the course in conjunction with one another.
2. My emotions.
My attitude going in was, "i'm going to turn this 89% into a 90%", and as soon as I reached the question above and the answer didn't flow as quickly as I had hoped, I had a little brain freak out and made stupid algebraic errors.

Variables out of my control
1. The random nature of the problems.
I felt like this exam pulled heavily from chapters 2-5 and just made the problems more difficult from these chapters instead of focusing on chapters 6-9. In my exam there were NO multiple choice or practice problems from chapter 8, which is the chapter I studied the most.

I am most likely going to do a rewrite if I get a mark lower than 70%, my best advice to you is be prepared to THINK! It might sound silly, but I went in expecting to regurgitate the info learned much like the midterm, but you will most likely be dealing with SOME problems never seen before where you must draw from what is learned in the course and apply it in new ways.

I am very interested to see how you find the final, please keep me updated on your thoughts!

 

[David89]

One thing that can be helpful when doing algebra is to resist putting in numbers until you have a formula for the final answer and are ready to evaluate it. There a few reasons for doing this including:

* If the terms cancel, it is easier to recognize if you have variable names.
* It usually makes the equations less cluttered.
* One is not tempted to combine the constants early and carry huge numbers of insignificant digits through the algebra.
* It is easier for the reader to know what each term means.
* It can make it obvious how the final answer depends on each of the givens of the problem.
* You can leave the units out of the algebra with more confidence, knowing that they are safely stashed away in the variables you are manipulating.

So instead of $5500\ tan 39 - 4.9t^2$ you could write $r\ tan \theta - \frac{1}{2}gt^2$.

Also, posting with embedded LaTeX makes for much more readable formulas.

Yea, the course goes through this and discusses the benefits of leaving out the variables until the final step.

This is my first ever physics course, and I have not done math in 7 years, so I get too excited and plug in too early cause I want the answer right away. I got to learn to be more patient!

 

[jfnn]

at the risk of making you nervous, I will say that I felt the exam was much harder than the midterms, assignments, and questions on the lab reports. I had 89% in the course going into the exam, and I'm not confident that I got a 65%.

I did all the assigned problems twice, the practice problems, and got an 85% on the practice final (self-assessed).

Variables I could have controlled,
1. My assumed attitude that the problems on the exam were going to be similar to the problems given in the textbook.
The problems on the practice final pull from several chapters at once and you have to utilize the tools learned in the course in conjunction with one another.
2. My emotions.
My attitude going in was, "i'm going to turn this 89% into a 90%", and as soon as I reached the question above and the answer didn't flow as quickly as I had hoped, I had a little brain freak out and made stupid algebraic errors.

Variables out of my control
1. The random nature of the problems.
I felt like this exam pulled heavily from chapters 2-5 and just made the problems more difficult from these chapters instead of focusing on chapters 6-9. In my exam there were NO multiple choice or practice problems from chapter 8, which is the chapter I studied the most.

I am most likely going to do a rewrite if I get a mark lower than 70%, my best advice to you is be prepared to THINK! It might sound silly, but I went in expecting to regurgitate the info learned much like the midterm, but you will most likely be dealing with SOME problems never seen before where you must draw from what is learned in the course and apply it in new ways.

I am very interested to see how you find the final, please keep me updated on your thoughts!

Thank you for your input. I'll let you know how it goes after I write it tomorrow.

Yeah this physics course, like math courses, builds on the foundations learned in the first chapters (1-5). It all comes back in the later chapters, which introduce variations to the earlier things mentioned.

I have read everything twice and done all the practice problems twice (I have even watched online lectures!) Hopefully, all my time put into this thing and keeping an open mind will get me through this!

 

[David89]

It sounds like you did a lot of work much like myself, I watched videos from Khan academy and put more into this course than I ever have for a course before, best of luck tomorrow

 

[David89]

Thanks to everyone who helped in this thread!

 

[cy123]

Hi, could you explain how you got the max height and final velocity? I am taking this course as well and my exam is on Friday, I'm really nervous so any help will be appreciated!

 

[Chestermiller]

Hi, could you explain how you got the max height and final velocity? I am taking this course as well and my exam is on Friday, I'm really nervous so any help will be appreciated!

@David89 How about you help this member?

 

[David89]

Sure!

Once you get t, you can plug t into your equation for V to solve for your initial vertical velocity.

Once you have initial vertical velocity, you can resolve your vector into horizontal and vertical components, and you can set the final velocity for vertical motion to zero (since Vf is zero when the projectile is at its highest point), and solve for delta y using Vf^2 = Vo^2 + 2a(deltay), since you now have the 3 variables needed to solve for the kinematic.

For the final velocity, I resolved the x-component and the y-component separately (x remains constant while y, starting from your max height, gets faster and faster until it finally hits the ground) and then used the pythagorean theorem to get Vf, and arctan(Vy/Vx) to get the final angle.

Hope this helps.

 

[cy123]

Sure!

Once you get t, you can plug t into your equation for V to solve for your initial vertical velocity.

Once you have initial vertical velocity, you can resolve your vector into horizontal and vertical components, and you can set the final velocity for vertical motion to zero (since Vf is zero when the projectile is at its highest point), and solve for delta y using Vf^2 = Vo^2 + 2a(deltay), since you now have the 3 variables needed to solve for the kinematic.

For the final velocity, I resolved the x-component and the y-component separately (x remains constant while y, starting from your max height, gets faster and faster until it finally hits the ground) and then used the pythagorean theorem to get Vf, and arctan(Vy/Vx) to get the final angle.

Hope this helps.

Thanks, it helped a lot!
Do you think this question will be on my final exam as well? I was expecting the final to consist of mostly questions from the second half of the course so now I'm nervous since you said that Chapter 8 material did not appear on your exam.

 

[David89]

It's difficult to say, I've only written one final from Athabasca for physics and this one was it.

The questions connect areas from the whole course and introduces new questions never dealt with, so definitely bring your brain to the exam and don't expect to simply memorize the info or regurgitate it onto the final.

I will say that no questions were from Chapter 8 on my exam, which I was a little surprised about because chapter 8 was by far the longest chapter in the course.

I'm not certain, but I think that the exam varies for each version by quite a bit, meaning that one version would consist of no chapter 8 questions, and another could have 3 out of the 6 long answer from chapter 8.

I think that this is due to the fact that the course is online, and it would be simple to exchange answers and strategies if all the exams were very similar.

I also think that this is why Athabasca offers rewrites so readily, I think they know that its possible to just have a "bad exam", and they offer up the chance to take the exam again if desired.

 

[cy123]

It's difficult to say, I've only written one final from Athabasca for physics and this one was it.

The questions connect areas from the whole course and introduces new questions never dealt with, so definitely bring your brain to the exam and don't expect to simply memorize the info or regurgitate it onto the final.

I will say that no questions were from Chapter 8 on my exam, which I was a little surprised about because chapter 8 was by far the longest chapter in the course.

I'm not certain, but I think that the exam varies for each version by quite a bit, meaning that one version would consist of no chapter 8 questions, and another could have 3 out of the 6 long answer from chapter 8.

I think that this is due to the fact that the course is online, and it would be simple to exchange answers and strategies if all the exams were very similar.

I also think that this is why Athabasca offers rewrites so readily, I think they know that its possible to just have a "bad exam", and they offer up the chance to take the exam again if desired.

Alright, I'll be sure to study for every chapter then just incase. Thank you for the help and the advice, I really appreciate it!

 

[akg402]

I just started this course and am writing a midterm on the 26th, I found that doing every single end of chapter question is becoming really time-consuming. Would you guys say understanding the concepts behind the assigned practice questions, assignment, and practice midterm is a good way to prepare for the exam instead of repeating all the end of the chapter questions?

 

[David89]

I ended up getting an A- in the course and I would say that an emphasis on conceptual understanding is FAR MORE important than continuous drilling.

In fact, I would say that the continuous drilling prevented me from getting a better grade because when it came time for the exam and my response wasn't automatic I panicked.

That being said, this was my first physics/math centric course, and I firmly believe that everyone needs to find out how they learn best.

If you can learn the material and apply the concepts, that's the best option.

If you're a little scared a want to do questions over and over to get the algebra down and approach the course in a more mechanistic style, go for it, but you will have to sew concepts together and think outside the box to get the right answer eventually, usually this happens during the final.

All the best with the course, I personally really enjoyed it.