Question

two particles moving in uniform gravitational field with an acceleration g. At the initial movement particles are located at the same point and moved with velocity u1=40ms^-1 and u2=10ms^-1 horizontally in opposite direction the time between the particles at the movement when there when their velocity vectors are mutually perpendicular in seconds is​

Answer 1

Let the particles project as given in above figure.

The vertical velocities of both the particles after time t would be

v=0+gt=gt

Let i,j the angles the projectiles form with vertical axis.⟹tan i = -3/gt and tan j = 4/gt

When the projectiles are perpendicular to each other, i + j = 90∘

tan( i+ j ) = 1+tan i tan j / 1+tan i tan j = ∞

⟹tan i tan j = −1

⟹gt= √12

Distance between the particles = 3t+4t=

7t=7 √12/g=2.5m