According to the question,
In two dimension, the position vectors r1 and r2 represented as
r1=vt−‌gt2...(i) r2=vt(−)−‌gt2()....(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+‌4g2t4=0 (where,
.⋅=⋅=⋅=1) v2t2=‌g2t4 ⇒v2=‌g2t2 ∴ Magnitude of velocity of the particles,
v=‌gt We know that, separation distance between particles at a time
t ∆x=2vt ∆x=2×v×‌⇒∆x=‌