Projectile Motion Q (1 Viewer)

gr_111

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Question from Maths in Focus, Ex 6.11 Q25. Part b is stuffing me around, can anyone help!

 

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Find their respective Cartesian Equations, then solve them simultaneously (for the two paths to meet).
 

gr_111

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Just checking, would the horizontal velocity of the second ball be given by the following?

 

Carrotsticks

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Just checking, would the horizontal velocity of the second ball be given by the following?

Not quite. It would just be x(dot)=-20cos45.

You add the +30 afterwards when you integrate one more time, to get x (since t=0, x=30)
 

gr_111

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I keep mucking this one up, does anyone else want to give it a bash?!
 

D94

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I keep mucking this one up, does anyone else want to give it a bash?!
More often than not, it comes down to your equations of motion and whether they are correct or not. After that, it's about thinking what is happening. What are your equations of motion? i.e. x = ..... y = ..... etc.
 

gr_111

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OK this is what I got for the equations of motion:

Projectile A (from the origin)
x.. = 0
x. = 15cos60
x = 15tcos60

y.. = -10
y. = -10t + 15sin60
y = -5t^2 +15tsin60


Projectile B (from x=30)
x.. = 0
x. = -20cos45
x = -20tcos45+30

y.. = -10
y. = -10t + 20sin45
y = -5t^2 +20tsin45
 

gr_111

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Don't worry, got this out finally. Turns out the best way is to equate the x displacements to find a time where they are at the same displacement. Sub the time into the x and y displacements to see what times they arrive at the points and hence whether they collide.
 
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Just tried the question...did you get for the 15m/s one y=8.4095m when they 'meet (in the x direction)' and y=9.997m for the 20m/s one?
 

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I am still stuck on this question been spending a couple of hours on it for curiosity sakes.


My first question to anyone that has attempted this, are the diagrams shown on Q25 misleading? First of all I worked out the height of the 15m/s (at 60 degrees) having a max height of 8.43 m and the second ball of 20 m/s (at 45 degrees) to be a height of 10.0 m.

The diagrams show that the 20m/s has a lower height which I believe is wrong.

Thoughts ? Opinions?
 

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