VELOCITY 11 



If two velocities are represented ly the two sides of a triangle 

 taken in order, their resultant will be represented hy the third side, 

 taken in the direction from the, first side to the second side. 



For example, let OP^ OP 2 be two lines drawn through O to 

 represent, on any scale, the velocities of a mov- 

 ing point at instants t lf t 2 . Then P^P Z will, on 

 the same scale, represent the additional velocity 

 acquired by the point in this interval. 



For we can imagine a frame moving with 

 the uniform velocity OP l of the particle at 

 instant t r The velocity OP Z at instant t z may 

 be supposed compounded of the velocity OP X 

 of the frame and a velocity PP Z relative 

 to the frame. Obviously this latter is the increase of velocity. 



EXAMPLES 



1. A car is running at 14 miles an hour, and a man jumps from it with a 

 velocity of 8 feet per second in a direction making an angle of 30 with the 

 direction of the car's motion. What is his velocity relative to the ground ? 



2. A railway train, moving at the rate of 60 miles an hour, is struck by a 

 bullet, which is fired horizontally and at right angles to the train with a velocity 

 of 440 feet a second. Find the magnitude and direction of the velocity with 

 which the bullet appears to meet the train to a person inside. 



3. A ship whose head points northeast is steaming at the rate of 12 knots in 

 a current which flows southeast at the rate of 6 knots. How far will the ship 

 have gone in 2|- hours ? 



4. A train is traveling at the rate of 30 miles an hour, and rain falls with 

 a velocity of 22 feet per second at an angle of 30 with the vertical in the same 

 direction as the motion of the train. Find the direction of the splashes made 

 on the windows by the raindrops. 



5. A steamer's course is due south, and its speed is 20 knots ; the wind is 

 from the west, but the line of smoke from the steamer is observed to point in a 

 direction 30 east of north. What is the velocity of the wind ? 



6. A man rows across a stream a mile wide, pointing his boat upstream at 

 an angle of 30 with the bank. How long does he take to cross, if he rows with 

 a velocity of 4 miles an hour and if the current has an equal velocity ? 



7. A stream has a current velocity a, and a man can row his boat with a 

 velocity 6.. In what direction must he row, if he is to land at a point exactly 

 opposite his starting point ? And in what direction must he row so as to cross 

 in the shortest time ? 



