Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**rajinikanth0602****Member**- Registered: 2012-06-30
- Posts: 16

Consider X-Y plane as ground and gravitational field acts perpendicular to it.A particle is projectedwith a velocity ''v'' at an angle less than 45°from origin onto circle (x)²+(y-d)²=r² on X-Y plane.Find the solid angle made by all projectionsof particle onto every point on the circle.{range ''R'' of particle≥(d+r)}.

*Last edited by rajinikanth0602 (2012-12-25 01:40:07)*

Offline

**scientia****Member**- Registered: 2009-11-13
- Posts: 224

I think you mean and also you want .

Supposed the trajectory is angled

horizontally from the vertical plane through theThen the solid angle you want is:

*Last edited by scientia (2012-12-26 15:22:48)*

Offline

**scientia****Member**- Registered: 2009-11-13
- Posts: 224

I made some careless mistakes in my calculations and got some horrendously frightening values for the elevating angle.

I have re-computed them. They should be

and

And you want to find the following integral for the solid angle:

*Last edited by scientia (2012-12-26 16:00:19)*

Offline

**scientia****Member**- Registered: 2009-11-13
- Posts: 224

I found some more errors and corrected them. And now I'm sure everything up there is perfect.

The challenge now is to compute the actual integral. Not for the faint-hearted.

*Last edited by scientia (2012-12-26 15:55:30)*

Offline

Pages: **1**