DYNAMICS. 51 



96. The greatest altitude above the point of pro- 

 jection, to which a projectile can ascend, is equal 

 to the height corresponding to its initial velocity, 

 multiplied into the square of the sine of the eleva- 



tion. that is, to -!L. sin E 2 . Also the time of its 



flight from the moment of projection till it strike 

 the horizontal plane passing through the point of 



21 c 

 projection, is x sin E. 



o 



The greatest height to which the projectile ascends is 

 therefore as the square of the velocity, multiplied in- 

 to the square of the sine of the elevation ; and the 

 time of the flight is simply as the velocity, multiplied 

 into the sine of the elevation. 



97. A projectile thrown with a given velocity, 

 from a point in a plane, will go to the greatest 

 distance on that plane, when its direction bisects 

 the angle which the plane makes with the verti- 

 cal. 



98. The points of greatest distance at which a 

 projectile, thrown with a given initial velocity, will 

 strike the different planes in the last proposition, 

 are all in a parabola given in position. 



