Nov 2009
#14
the easiest method seemed to be substitution here.
assume m=2, Initial v= 4,
so E(initial)= 1/2 *mv^2= 16 joules
now at the top, the vertical component of velocity is 0. There is no acceleration in the horizontal direction, so the horizontal component of velocity (the only velocity at the top) is the same as the beginning.
This is v cos 45, again using v=4, horizontal component of velocity at the top= 4 cos 45
now find E at the top
E(new)= 1/2 * 2 * (4 cos 45)^2 = 8 joules
now compare the new E to the initial E. 8/16=1/2=====> 0.5E (The answer is A)....