DYNAMICS, EI.i: M 1 . N TARY. 



1308. A perfectly elastic particle is projected with a given 

 velocity from a given point in one of two planes, equally inclined 

 to the horizon and intersecting in a horizontal straight line ; deter- 

 mine the angle of projection in order that the particle may after 

 n-tl. ctiun return to the point of projection and be again reflected 

 in the same path. Prove that the inclination of each plane must 

 be 45. 



1 309. An imperfectly elastic particle let fall on a fixed inclined 

 plane bounds on to another fixed inclined plane, the line of inter- 

 section being horizontal, and the time between the two planes is 

 givm ; prove that the locus of the point from which the particle 

 is let fall is in general a parabolic cylinder ; but that it is a 

 plane if 



tan a tan (a + /?) = e, 



a, {} being the inclinations of the planes, and e the elasticity. 



1310. A particle is projected from a given point, and its 

 resolved velocity parallel to a given straight line is given ; prove 

 that the locus of the focus of the parabolic path is a parabola of 

 which the given point is the focus, and whose axis makes with the 



1 an angle double that made by the L light line. 



1311. A partirl,-, pn j. cted In mi a point in an inclined 

 plane, after the r th impact begins to move at right angles to the 

 plane, and at the n th impact is at the point of projection; pro\.- 



that 



e* - 2e r + 1 = 0, 

 ng the elasticity. 



l.;U. A ]. article is projected given point in a 1 



zontal plane at an angle a to tl . and. after one rvl 



, returns to the point of projection : prove that 

 p,int of impact must lie on the straight line 



./, // 1'fing measured hoi i vertically from the point of 



lion. If tin- N' Looitj of pn.jrciioii and not the dmrtimi be 

 , th- loeu-, of : i is an ell: 



\v. 18 



