Kinematics Question 596

Question: If $ V _{1} $ it’s velocity of a body projected from the point A and $ V _{2} $ it’s 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’t collide.

Show Answer

Answer:

Correct Answer: B

Solution:

[b] Two bodies will collide at the highest point if both cover the same vertical height in the same time.

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} $



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