Two particles 'A' and 'B' are projected in the vertical plane with same initial speed u 0 from position (0, 0) and ( λ , – h) towards each other as shown in figure at t = 0.
(i) The path of particle 'A' with respect to particle 'B' will be
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(i)b (ii)b (iii)c
Sol. (i & ii)
The path of a projectile as observed by other projectile is a straight line.
V A = u cos θ 
+ (usin θ – gt) 
. V AB = (2u cos θ ) 
V B = – u cos θ 
+ (u sin θ – gt) 
.
a BA = g – g = 0
The vertical component u 0 sin θ will get cancelled. The relative velocity will only be horizontal which is equal to 2u 0 cos θ .
Hence, B will travel horizontally towards left with respect to A with constant speed 2u 0 cos θ and minimum distance will be h.
(iii) Time to attain this separation will be 
.
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