BOOK OF MATHEMATICAL PROBLEMS. 



1362. A point describes a parabola in such a manner that 

 its velocity, at a distance r from the focus, is 



y, c being constant ; prove that its acceleration is compounded of 



fc* 

 /parallel to the axis, and y 8 from the focus. 



13G3. A point describes a semi ellipse bounded by the minor 

 axis, and its velocity at a distance r from the focus is 



|r(2a-r) 



where 2a is the length of the major axis, and /a constant accelera- 

 tion ; prove that the acceleration of the point is compounded of 

 two, each varying universely as the square of the distance, one 

 tending to the nearer focus and the other from the farther focus. 



1364. A point is describing a circle, and its velocity at an 

 angular distance from a fixed point on the circle valies as 



N/(l + COS' 0). 



sin* 6 ' 



prove that its acceleration is compounded of two tending to fixed 

 points at the extremities of a diameter, each varying inversely as 

 the fifth power of the distance and equal at equal distances. 



1365. A point describes a circle, under acceleration constant 

 and not tending to the centre ; prove that the point oscillates 

 through a quadrant, and that the direction of the acceleration 

 always touches a certain hypocycloid. 



1366. A parabola is described with accelerations F, A, 

 tending to the focus and parallel to the axis respectively ; prove 

 that 



r being th.e focal distance. 



