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Parametric equation application?

  • Thread starter lisbon
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  • #1
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Homework Statement



http://i.imgur.com/oogkT4K.png


Homework Equations



y = (x-h)^2 + k

The Attempt at a Solution




y = (x-95)^2 + 10 ??? We were assigned this in class but my teacher never taught us anything about these kinds of problems. I've learned basic parabolas and equations in class but I don't know how to apply it to this assignment because the cannonball lands in the net at a different height from the original platform. I also have no idea how to find the angle of the cannon. Can someone help me out? Thanks!
 

Answers and Replies

  • #2
verty
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Homework Statement



http://i.imgur.com/oogkT4K.png


Homework Equations



y = (x-h)^2 + k

The Attempt at a Solution




y = (x-95)^2 + 10 ??? We were assigned this in class but my teacher never taught us anything about these kinds of problems. I've learned basic parabolas and equations in class but I don't know how to apply it to this assignment because the cannonball lands in the net at a different height from the original platform. I also have no idea how to find the angle of the cannon. Can someone help me out? Thanks!
You have two points on the parabola, the cannon and the camera. I would assume the camera pole is at the front of the net and the camera's mounting point is on the parabola.

So the parabola goes through those points and you are given the velocity. See if you can find the strategy now to solve this. These questions are notoriously difficult and if you haven't learned them, I think you won't be able to solve it.
 
  • #3
LCKurtz
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You have two points on the parabola, the cannon and the camera. I would assume the camera pole is at the front of the net and the camera's mounting point is on the parabola.

So the parabola goes through those points and you are given the velocity. See if you can find the strategy now to solve this. These questions are notoriously difficult and if you haven't learned them, I think you won't be able to solve it.
I don't see any reason to assume the camera itself is on the trajectory. I think it is at a given height and you smile at it when you are at that height on the way down. It looks to me like you vary the barrel angle to hit between the near and far end of the net and pick among them for max height.
 
  • #4
LCKurtz
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Here's an animated gif showing the trajectory for various cannon angles. It looks like a doable problem to me, at least with the help of Maple.

attachment.gif
 

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  • #5
verty
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I don't see any reason to assume the camera itself is on the trajectory. I think it is at a given height and you smile at it when you are at that height on the way down. It looks to me like you vary the barrel angle to hit between the near and far end of the net and pick among them for max height.
I was unsure of how to interpret that the performer must look directly into the camera, but yes, if the camera pans to follow him, he can just look at the camera from wherever he happens to be when he is at that height.

The maximum height is clearly increasing with angle so the solution will be at one of the extreme points of the net or at an angle of 60 degrees. So two points and one angle to plug in, no calculus required. It's certainly doable but compared to the typical homework problems in this section, it is quite difficult. And for readers who don't know projectile motion which isn't always taught in school, these are notoriously difficult questions, at least they were for me.

Also I didn't want to give a hint because the title was about applying parametric equations and I thought the only good hint I could give was to show how to apply them. So I didn't give a hint but I wanted to point out that this is a difficult question and completing it without experience would be pretty tough.
 

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