 # two particle A and B r initially located at same point in uniform gravitational field of earth . At a certain moment they r projected with speed v  and v  horizontally in opposite direction the saperation between them at that moment when their velocity vector become perpendicular to each other. Puneet Mittal AskiitiansExpert-IITD
22 Points
12 years ago

Hi Khushboo,

The Answer to the above question is as follows :

Let A travels towards left and B travels towards right.

When their velocities are perpendicular with each other, Let angles of velocity vectors Va and Vb be α and β  with horizontal,

Thus tanα = Vay / Vax

Vay = 0 - g*t  Vax = v in left direction

tanα = 1/(v)*g*t   (considering only magnitudes)

And tanβ = Vby / Vbx

Vby = 0 - g*t  , Vbx = v in right direction

Thus tanβ = 1/(v)*g*t    (considering only magnitudes)

Thus tanα = tanβ

or  α = β

Also  α + β = 90 degree , ( As the velocites are perpendicular,  α + 90 + β  = 180 degree if you draw the diagram )

Thus  α = β = 45 degrees upon solving above eqns.

Speration between them at this point is Distance travelled by a in left hroizontal direction +  Distance travelled by b in right hroizontal direction

S = separation = Vax*t + Vbx*t = 2vt

tan45 degrees = 1 , Thus 1 = gt/v or t = v/g

Hence S = 2v*v/g = 2v2/g is the Answer