Two balls are thrown horizontally from the top of a tower with velocities v1 and v2 in opposite directions at the same time. After how much time, the angle between velocities of balls becomes 90o?

General velocity vector of the projectiles is given by
→V = v1 + j(gt) .. (1)
→V = v2 + j(gt) (2)
for both the vectors above to be perpendicular, their dot product must be zero.
hence, dot product is
v1 × v2 + g²t² = 0
finally, t = √v1v2/g