56 KINEMATICS. [114. 



114. Exercises. 



(1) A body falls from rest at a place where g= 32.2. Find (a) the 

 velocity at the end of the third second ; (b) the space fallen through in 

 5 seconds ; (c) the space fallen through in the fifth second. 



(2) If a railroad train, at the end of 2 m. 40 s. after leaving the 

 station, has acquired a velocity of 30 miles per hour, what was its accel- 

 eration (regarded as constant) ? 



(3) Galilei, who first discovered the laws of falling bodies, expressed 

 them in the following form : (# ) The velocities acquired at the end of 

 the successive seconds increase as the natural numbers ; (^) the spaces 

 described during the successive seconds increase as the odd numbers ; 



(c) the spaces described from the beginning of the motion to the end 

 of the successive seconds increase as the squares of the natural num- 

 bers. Prove these statements. 



(4) A stone dropped into the vertical shaft of a mine is heard to 

 strike the bottom after / seconds ; find the depth of the shaft, if the 

 velocity of sound be given = c. Assume / = 4 s., c 332 metres, g = 980. 



(5) A railroad train approaches a station with uniformly retarded 

 motion. During the first two minutes of its retarded motion it makes 

 3960 ft.; during the next minute 990 ft. (a) When will it come to 

 rest? (b) What is the retardation? (c) What was the initial velocity? 



(d) When will its velocity be 4 miles an hour? 



(6) Interpret equations (6) and (7) geometrically. 



(7) A body being projected vertically upwards with an initial velocity 

 VQ, (a) how long and (b) to what height will it rise ? (V) When and 

 (</) with what velocity does it reach the starting-point ? 



(8) A bullet is shot vertically upwards with an initial velocity of 

 1600 ft. per second, (a) How high will it ascend? (b) What is its 

 velocity at the height of 32,000 ft.? (c) When will it reach the ground 

 again? (d 7 ) With what velocity? (e) At what time is it 32,000 ft. 

 above the ground ? (/) Explain the meaning of the * double signs 

 wherever they occur in the answers. 



(9) With what velocity must a ball be thrown vertically upwards to- 

 reach a height of 100 ft. ? 



(TO) A body is dropped from a point A at a height AB=h above 

 the ground ; at the same time another body is thrown vertically 



