74 KINEMATICS. [145. 



(6) Construct the tangent to any conic section when a directrix anc 

 the corresponding focus are given. 



(7) Two trains of equal length pass each other with equal velocity 

 -on parallel tracks. A man riding on a bicycle along the track at the 

 rate of 8 miles an hour notices that the train meeting him takes 

 seconds to pass him, while the other takes 6 seconds. Find the 

 velocity of the trains. 



(8) A swimmer, starting from a point A on one bank of a river 

 wishes to reach a certain point B on the opposite bank. The velocity 

 # 2 of the current and the angle made by AB with the direction of the 

 -current being given, determine the least relative velocity i\ of the 

 swimmer in magnitude and direction. 



(9) Two men, A and B, walking at the rate of 3 and 4 miles an hour 

 respectively, cross each other at a rectangular street corner. Find the 

 relative velocity of A with respect to B in magnitude and direction. 



(10) A man jumps from a car at an angle of 60 with a velocity o 

 & feet a second (relatively to the car). If the car be running 10 miles 

 an hour, with what velocity and in what direction does the man strike 

 the ground? 



(n) The point J\ moves with constant velocity v along the line 

 PiQ. In what direction JP 2 Q must a point P 2 move with constan 

 velocity v. 2 in order to meet PJ What is the locus of Q when the 

 direction of P l Q varies ? When is the solution impossible ? 



(12) A point Amoves uniformly in a circle, while another point 

 moves with equal velocity along a tangent to the circle. Find the 

 relative path of either point with respect to the other. 



(13) The velocity of light being taken as 300,000 kilometres per sec 

 ond, and the velocity of the earth in its orbit as 30 kilometres, determine 

 approximately the constant of the annual aberration of the fixed stars. 



2. APPLICATIONS. 



145. The motion of the piston of a steam engine furnishes 

 interesting illustrations of the application of graphical methods 

 in kinematics. 



In Fig. 35, let OQ=a be the crank arm, PQ = l=ma thi 

 -connecting rod, P 1 P 2 = s the " stroke," so that l=ma = %m 



