.90 KINEMATICS. [168 



(4) The range of a projectile is the distance from the starting poin 

 to the point where it strikes the ground. Show that on a horizonta 



v 2 

 plane the range is R = 2 a = sin 2 e. 



o 



(5) The time of flight is the whole time from the beginning of the 

 motion to the instant when the projectile strikes the ground. It is 

 best found by considering the horizontal motion of the projectile alonej 

 which is uniform. Show that on a horizontal plane the time of flight is 



7V=sine. 

 g 



(6) Show that the time of flight and the range on a plane through 

 the starting point inclined at an angle to the horizon are 



r_2Vo sin(c 6) A r, _ 2zy* sin(e 0)cose 

 j. Q -- - ana Ytg 



g cos g cos 2 9 



(7) What elevation gives the greatest range on a horizontal plane? 



(8) Show that on a plane rising at an angle to the horizon, to obtain 

 the greatest range, the direction of the initial velocity should bisect the 

 angle between the plane and the vertical. 



(9) A stone is dropped from a balloon which, at a height of 1000 ft., 

 is carried along by a horizontal air-current at the rate of 15 miles an 

 hour, (a) Where, (b) when, and (c) with what velocity will it reach 

 the ground ? 



(10) What must be the initial velocity V Q of a projectile if with art 

 elevation of 30 it is to strike an object 100 ft. above the horizontal 

 plane of the starting point at a horizontal distance from the latter of 

 1200 ft.? 



(n) What must be the elevation e to strike an object 100 ft. above 

 the horizontal plane of the starting point and 5000 ft. distant, if the 

 initial velocity be 1200 ft. per second? 



(12) Show that to strike an object situated in the horizontal plane of 

 the starting point at a distance x from the latter, the elevation must be 

 e or 90 e, where = ^sin 



(13) The initial velocity V Q being given in magnitude and direction, 

 show how to construct the path graphically. 



