86 KINEMATICS. [165. 



We have therefore simply a rectilinear motion with the constant 

 acceleration gs'mO, so that all the formulae of Art. 107-113 

 will here apply if for the acceleration j (or g) we substitute 

 "sin#. 



Thus, if the initial velocity be o, the motion is determined 

 by the equations 



(i) 



*, (2) 



. (3) 



165. If there be an initial velocity T/ O parallel to the line of 

 greatest slope of the inclined plane, the equations are 



(I') 



, (2') 



where ^ is to be regarded as positive if its direction is down 

 the plane and negative when up the plane. 



If the initial velocity V Q be inclined to the plane at an 

 angle ft, it can be resolved into the components z> cos/3 and 

 VQ sin ft, the former alone being effective so that v cos ft must 

 be substituted for v in the above formulae. 



166. Exercises. 



(1) A railroad train is running up a grade of i in 250 at the rate of 

 15 miles an hour when the coupling of the last car breaks. Neglecting 

 friction, (a) how far will the car be after two minutes from the point 

 where the break occurred ? (<) When will it begin moving down the 

 grade? (c) How far behind the train will it be at that moment? 

 (d) If the grade extend 2000 ft. below the point where the break 

 occurred, with what velocity will it arrive at the foot of the grade ? 



(2) Show that the final velocity is independent of the inclination of 

 the plane; in other words, in sliding down a smooth inclined plane a 



