214 



MOTION UNDER CONSTANT FORCES 



2. Find what area of a vertical wall can be covered by afire-hose projecting 

 water with velocity v at a distance h from the wall 



Let S be the nozzle of the fire-hose, and le 

 us regard it as capable of projecting particl 

 of water in any direction we please with 

 velocity v. The points which can be read 

 will, by 172, be all the points which lie insic 

 a paraboloid of revolution having its axis v< 



tical, S for focus, and latus rectum If 



^ take S as origin, and the vertical through 

 |j for axis of z, the equation of this paraboloi 

 |j will be 



Fia. 1*5 



f. 



The curve in which this cuts the vertical wall, of which the equation m 

 be taken to be y = A, will be 



or 



g \2g 2i)2 Z )' 



2 I) 2 



This is a parabola, of latus rectum - , having its axis vertical, and it 

 vertex at a height 



2g 2v 2 



above S. All the points inside this parabola will be within range of the jet of 

 water. The points on the wall which are outside this parabola will b 

 inaccessible. 



EXAMPLES 



1. A revolver is fired horizontally from the top of a tower 100 feet high, th 

 bullet leaving the muzzle with a velocity of 600 feet per second. Where will th 

 bullet strike the ground ? 



2. A rifle bullet, fired horizontally at a height of 10 feet above the surface o 

 a lake, strikes the water at a distance of 600 yards. Find its velocity in fee 

 per second, the resistance of the air being supposed negligible. 



3. Prove that the claim for a rifle, that the bullet does not rise more thai 

 one inch in a range of 100 yards, implies that the velocity must be greater thai 

 2078 feet per second. 



4. Find the greatest range on a horizontal plane of a cricket ball throwi 

 with a velocity of 100 feet per second. 



