MC --Projectile motion

2007-10-13 9:33 pm

A stone is projected at an angle of 45 ° to the horizontal with an intial kinetic energy E .
Neglecting air resistance ,when the stone is halfway up,its kinetic energy is

A . E/4
B.E/2
C.3E/4
D. E/ √2
E. √E

Please show your detailed workings.

回答 (1)

Pun

2007-10-14 2:28 am

✔ 最佳答案

I believe the answer should be "C" 3E/4.

Since it is projected at 45 degree
initial KE due to horizontal speed = initial KE vertical = 1/2 [1/2 m v^2]
KE (horizontal) + KE (vertical) = KE (overall)
(v is certainly the initial velocity)

KE (horizontal) does not change during the flight,
while KE (vertical) changed to a half at a height "half way up".
so, KE (vertical) becomes 1/2 * 1/2 * 1/2 mv^2

Hence, at half way up:
KE (vertical) = 1/4 E
KE (horizontal) = 1/2 E
KE = (1/4 + 1/2) E = 3E/4

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