DYNAMICS, ELEMENTARY. 271 



1296. In the system of pullies in which each hangs by a 

 separate string, P just supports IP; prove that, if P be replaced 

 by another weight Q, the centre of gravity of Q and W will descend 

 "with uniform acceleration 



W(Q-Pf 



the weights of the pullies being neglected. 



1297. The radii of two circles whose centres are in the same 

 horizontal line are a, 6, and the distance between their centres 

 c(>a + 6); prove that the shortest time of descent from one to 

 the other down a straight line is 



/ ,2 *-(a + l>y\ 

 V W +& /' 



1298. A parabola is placed with its axis horizontal; prove 

 that the time of shortest descent down a straight line from the 



curve to the focus is / , I being the latus rectum. 

 V 3 



1299. An ellipse is placed with its major axis vertical ; prove 

 that the straight line of quickest descent from the curve to the 

 lower focus is equal in length to the latus rectum, provided the. 



ricity be >. 



1300. A uniform string of length 2<* is in equilibrium, passing 

 I small smooth pulley; if it bo just .1, the velocity 



of the string when the whole has just passed the pulley is >Jag. 



II. Parabolic Motion. 



1301. A heavy particle is projected in a given direction, 

 (let ermine its velocity in order that it may pass through a fixed 



point. 



