228 MOTION OF SYSTEMS OF PARTICLES 



8. A mass of 8 pounds moving north at a speed of 10 feet per second is struck 

 by a mass of 6 pounds moving east at 14 feet per second, and its direction of 

 motion is thereby deflected through 30 degrees, while its speed is increased by 

 1 foot per second ; show that the velocity of the other is diminished by 7.3 feet 

 per second, approximately, and find its new direction of motion. 



9. Two ice yachts, each of mass M, stand at rest on perfectly smooth ice, 

 with their keels in the same direction. A man of mass m jumps from the first 

 to the second, and then immediately back again on to the first. Show that the 

 final velocities of the yachts are in the ratio of M + m : M. 



KINETIC ENERGY 



183. We may best begin the study of the kinetic energy of a 

 system of particles by drawing attention to a difficulty which has 

 not so far been encountered in the present book. This difficulty 

 will be best illustrated by a particular example. 



Suppose that a ship is moving through the water with a velocity 

 of 20 feet per second, and that a person on deck throws a ball of 

 mass m forward with a velocity of 30 feet per second relative to 

 the ship. If the person were fixed in space, we might say that the 

 work he did was equal to the final kinetic energy of the ball, and 

 was therefore Jw(30) 2 , or 450 m. 



. On board ship, however, the ball originally had a velocity of 20 

 and the thrower increases this velocity to 50. The change in the 

 kinetic energy of 'the ball is accordingly 



lm(50) 2 -lm(20) 2 , 



or 1050 m. If this represents the work done by the thrower, then 

 we are driven to suppose that it would be more than twice as 

 hard to throw the ball on board ship as on land. This would 

 clearly be erroneous. 



184. The error lies in this, that the thrower not only imparts a 

 velocity to the ball but also to the ship. If he throws the ball 

 forward he must, from the principle of conservation of momentum, 

 impart a backward velocity to the ship, of momentum equal and 

 opposite to the forward momentum of the ball. The total work per- 

 formed is equal to the change produced in the total kinetic energy 

 of the ship and the ball. 



