WBJEE 2019 Physics Solved Paper

According to the question,In two dimension, the position vectors r1 and r2 represented as
r1=vt

⋀

i

−‌

1

2

gt2

⋀

j

...(i)
r2=vt(−

∧

i

)−‌

1

2

gt2(

∧

j

)....(ii)
∵ We know that, when the two vectors are mutually perpendicular, i.e.
θ=90°
So
r1⋅r2=r1r2‌cos‌90∘
r1⋅r2=0
Substituting the values r1 and r2 in the above relation, we get
−v2t2+‌

1

4

4g2t4=0 (where, .

∧

i

⋅

∧

i

=

∧

j

⋅

∧

j

=

∧

k

⋅

∧

k

=1)
v2t2=‌

1

4

g2t4
⇒v2=‌

1

4

g2t2
∴ Magnitude of velocity of the particles, v=‌

1

2

gt
We know that, separation distance between particles at a time t
∆x=2vt
∆x=2×v×‌

2v

g

⇒∆x=‌

4y2

g