EXAMPLES 25 



15. A ball is thrown from the top of a building with a velocity of 64 feet 

 per second at an angle of 30 with the horizontal in an upward direction. 

 Find the directions of its motion at the end of the first and second seconds, 

 and also the velocities at these instants. 



16. A ball is tossed into the air with a velocity of 20 feet a second, and 

 at the end of a second is seen to be moving in a line at right angles to the 

 direction of projection. What is its velocity at the instant? 



17. If the velocity of a bullet is supposed to be a uniform horizontal 

 velocity equal to n times that of sound, show that the points at which the 

 sounds of the firing and of the bullet striking the target are heard simul- 

 taneously lie on a hyperbola of eccentricity n. Examine the case in which 

 n is very nearly equal to unity. 



18. Assuming that the earth moves in a circular orbit about the sun 

 with a velocity 29.6 kilometers per second, and that the velocity of light 

 is 300,000 kilometers per second, 'find the apparent displacement of the sun 

 due to the earth's motion. 



19. Assuming that the earth in a year describes a circle uniformly 

 about the sun as center, that the distance between the centers is 220 radii 

 of the sun, and that the radius of the sun is 108 times that of the earth, 

 find the velocity of the vertex of the earth's shadow, taking the sun's 

 radius as the unit of space and a year as the unit of time. 



