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# Mechanics 2 Projectile motion question watch

1. Hi there,
I'm stuck on this question regarding littlewood coordinates:
A particle P is projected from a point O with speed V and at an angle theta to the horizontal. The line OQ corresponds to the orginal direction of the particle and QP is the vertical line thorugh the particle at time t. The lengths OQ and OP are called the Littlewood coordinates of P and are represented by E and N.

a). Show that E and N are independent of theta
Ive done this:

OQ= sqrt((Vcostheta)^2 +(Vsintheta)^2)
which simplifies to V since cos^2+sin^2=1
No theta, so OP is independent of theta.

OP= sqrt(Vtcostheta)^2+(Vtsintheta-0.5gt^2)^2)
and i get sqrt(t^2V^2+gvt^3sintheta+0.25g^ 2t^4)
I dont know how to get this part to be free of sintheta

b). Use littlewood coordinates, together with the sine rule, to find the time of flight of the particle.
Don't even know where to begin here.

This is in the Oxford Oxbox textbook for Edexcel.

2. (Original post by kennz)
Hi there,
I'm stuck on this question regarding littlewood coordinates:
A particle P is projected from a point O with speed V and at an angle theta to the horizontal. The line OQ corresponds to the orginal direction of the particle and QP is the vertical line thorugh the particle at time t. The lengths OQ and OP are called the Littlewood coordinates of P and are represented by E and N.

a). Show that E and N are independent of theta
Ive done this:

OQ= sqrt((Vcostheta)^2 +(Vsintheta)^2)
which simplifies to V since cos^2+sin^2=1
No theta, so OP is independent of theta.
You've missed the "t"

OP= sqrt(Vtcostheta)^2+(Vtsintheta-0.5gt^2)^2)
and i get sqrt(t^2V^2+gvt^3sintheta+0.25g^ 2t^4)
I dont know how to get this part to be free of sintheta

b). Use littlewood coordinates, together with the sine rule, to find the time of flight of the particle.
Don't even know where to begin here.

This is in the Oxford Oxbox textbook for Edexcel.

I suspect it is QP that you should be looking for, rather than OP.

I can't find anything on Littlewood coordinates on the 'net that might explain things.

Do you have anything further in the book; in the question or prior to it?
3. surprisingly little about these coordinates on google...
4. Following on from Ghostwalkers correction,

let the position on the ground vertically below the particle be called F.
Let the position of the particle be P.
Use suvat to find the altitude of the particle at time t .. you have now found PF.

consider the triangle OQP, you already know OQ, hence the distance N will be QF-PF.
Use right angled trig. to get QF. Subtract PF and you have the result independent of theta.
5. No the t shoudnt be there since its the orginal direction of the particle which is at t=0. Theres nothing else in the book, if you copy and paste the question inton google there is a textbook viewer that has a very similar question, but the page with the solution is blocked
6. (Original post by kennz)
No the t shoudnt be there since its the orginal direction of the particle which is at t=0. Theres nothing else in the book, if you copy and paste the question inton google there is a textbook viewer that has a very similar question, but the page with the solution is blocked
If you leave the t out, then you're saying OQ has a fixed length, and so the vertical through the particle at time t, is also fixed, i.e. the particle is frozen in space. Don't think so.
7. (Original post by ghostwalker)
If you leave the t out, then you're saying OQ has a fixed length, and so the vertical through the particle at time t, is also fixed, i.e. the particle is frozen in space. Don't think so.
Ah right I get you, thanks
8. (Original post by dpm)
Following on from Ghostwalkers correction,

let the position on the ground vertically below the particle be called F.
Let the position of the particle be P.
Use suvat to find the altitude of the particle at time t .. you have now found PF.

consider the triangle OQP, you already know OQ, hence the distance N will be QF-PF.
Use right angled trig. to get QF. Subtract PF and you have the result independent of theta.
Can you show me what you'd do for QF, I got vtsintheta by using the coordinates of Q which are (vtcostheta,vtsintheta) and the coordinates of F which are(Vtcostheta,0).

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