Kinematics Question 596
If $ V _{1} $ is the velocity of a body projected from point A and $ V _{2} $ is the velocity of a body projected from point B, which is vertically below the highest point C. If both the bodies collide, then
Options:
A) $ {V} _{1}=\frac{1}{2}{V} _{2} $
B) $ {V} _{2}=\frac{1}{2}{V} _{1} $
C) $ {V} _{1}={V} _{2} $
D) Two bodies can collide.
Show Answer
Answer:
Correct Answer: B
Solution:
Two bodies will collide at the highest point if both cover the same vertical height in the same time interval.
So, $ \frac{V _{1}^{2}{{\sin }^{2}}30{}^\circ }{2\cancel{g}}=\frac{V _{2}^{2}}{2\cancel{g}} $
$ \Rightarrow \frac{V _{2}}{V _{1}}=\sin 30{}^\circ =\frac{1}{2} $
$ \therefore V _{2}=\frac{1}{2}V _{1} $
BETA
