i;o.] PLANE MOTION. g x 



(14) If it be known that the path of a point is a parabola and that 

 the acceleration is parallel to its axis, show that the acceleration is 

 constant. 



(15) Prove that a projectile whose elevation is 60 rises three times 

 as high as when its elevation is 30, the magnitude of the initial velocity 

 being the same in both cases. 



(16) Construct the hodograph for parabolic motion, taking the focus 

 as pole and drawing the radii vectores at right angles to the velocities. 



169. A projectile moving in the air or in any other resisting 

 medium of uniform density is subject, in addition to the con- 

 stant acceleration g of gravity, to the resistance of the medium 

 which produces a retardation variable both in magnitude and 

 direction (Art. 125). Experiment shows that this retardation 

 jean he expressed in the form cv n , where c is constant for a given 

 projectile and medium, and n must be determined by experiment 

 for different initial velocities. 



170. For n=i the integrations can be readily effected. 

 Resolving tbe retardation cv into its components cv x =cdxjdt, 



y cdyjdt, the equations of motion are 



d^x dx d*y dy 



- = ~ c - c 



Integrating, we find 



^=^ = ^0 cos *-", v y = ^-= l -[-g+(cv^me+g)e- ct ], (9) 

 ctt dt c 



since for tQ we have v x = v$ cose, z/ y = z/ sin e. 

 The second integration gives 



(10) 



