ILLUSTRATIVE EXAMPLE 227 



The components of actual velocity of the shot are 



M 



u Fcosa, 

 M + m 



v F sin a. 

 Thus the actual velocity of the shot is 



= r m(23f + m) f 



(M+m)* 



while the angle of elevation, 0, is given by 



v M + 



u M 



^ 

 tana. 



EXAMPLES 



./I. An empty railway truck weighing 8 tons, originally at rest, is run into by 

 a similar truck carrying a load of 24 tons and moving at the rate of a mile an 

 hour, and the two trucks then move on together. Find their common velocity. 

 - 2. A gun of mass M fires a shot of mass m horizontally. Show that of the 



work done by the powder, a fraction is wasted in producing the recoil 



of the gun. M + m 



^3. A particle of mass m slides down a smooth inclined plane of angle or, the 

 plane itself (mass M ) being free to slide on a smooth table. Find the acceleration 

 of the particle and the plane. 



4. A shell is observed to explode when at the highest point of its path. It 

 is divided into two equal parts of which one is seen to fall vertically. Prove 

 that the other will describe a parabola of which the latus rectum will be four 

 times the latus rectum of the original parabola. 



5. A shot of \ ounce weight strikes a bird of weight 6 pounds while in the 

 air. At the moment of striking, the shot has a horizontal velocity of 1000 feet 

 a second and the bird is flying horizontally in the same direction at a height of 

 64 feet above the ground, with a velocity of 20 feet a second. Show that the 

 bird will fall at a distance of about 62.2 feet beyond the place where it was 

 struck by the shot. 



6. A ship of 5000 tons steaming at 20 knots suddenly runs into a whale 

 whose weight is 12 tons, asleep on the surface of the water. By how much is 

 the ship's speed reduced ? (Neglect motion of water.) 



7. A mail package weighing 2 hundredweight is thrown out from a train 

 going at 60 miles an hour, with a horizontal velocity relative to the train of 11 

 feet per second at right angles to the track. It falls into a handcart of weight 

 3 hundredweight, which is free to move on a level platform, its wheels being 

 set so that its motion will make an angle of 30 degrees with the track of the 

 train. With what velocity will the cart start into motion ? 



