PRO 



xz 



?/ = A- tan. r 5. 



4 h cos. 2 



Cor. 2. To find where the curve meets the horizontal piano, we must 

 put y = o, .*. x tan. , T-T j = o, .'. # = 4<k tan. cos. 8 , zr 4 h 



j. ^* /i COS.* a. 



sin. cos. a = 2 h sin. 2 as,, which agrees with Art. 2. 



Cor. 3. If # does not enter the conditions of the problem, we have, by 



eliminating i 



gt* 

 y = x tan. , -. 



Cor. 4. To find the / which the curve makes with the horizon at any 

 in 



point. 



Let be this angle, tan. <p = - -, and differentiating the value of y, 



tan. a tan. c> . x . 

 2 h cos. 8 oe, 



Ex. 1. Let a body be projected from the top of a tower horizontally with 

 a velocity acquired in falling down its height j at what distance from the 

 base will it strike the horizon ? 



Here if a ==. altitude of tower, y a, z= o, and vz =. 2 g a, .'. 

 . a -^ , and # = 2 a. 



J?A\ 2. A body is projected at an / of 45, with a velocity of 50 feet per 

 second ; find its horizontal range. 



Here 45, v 50, .". when y o 



250 

 _ _. 



Ex. 3. A projectile is thrown across a plain 120 ject wide, to strike ;t 

 mark .'30 feet high, the velocity of projection being that acquired down 

 SO feet ; required the / of projection. 



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