# 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.

22 Points
13 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

Puneet

shashank mishra
14 Points
13 years ago