A) \[{{\text{V}}_{\text{1}}}\text{=}\frac{\text{1}}{\text{2}}{{\text{V}}_{\text{2}}}\]
B) \[{{\text{V}}_{2}}\text{=}\frac{\text{1}}{\text{2}}{{\text{V}}_{1}}\]
C) \[\,{{\text{V}}_{\text{1}}}\text{=}{{\text{V}}_{\text{2}}}\]
D) Two bodies can't collide.
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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