See the diagram for the way vectors are added and the angle that resultant makes.
with an angle Ф between them is given by the law of vector addition : V² = V₁² + V₂² + 2 V₁ V₂ Cos Ф
= V₁² given
=> V₂ = - 2 V₁ Cos Ф
---- (2) Angle δ between the resultant vector V and V₂
is given by :
Now , the magnitude of
is doubled. V₂ remains same. resultant V² = (2V₁)² + V₂² + 2 * 2V₁* V₂ * Cos Ф
= 4 V₁² + (-2V₁ Cos Ф)² + 4 V₁ (-2V₁ CosФ) Cos Ф
= 4 V₁² ( 1 - Cos² Ф) = 4 V₁² Sin² Ф | V | = | 4 V₁ Sin Ф | magnitude of the resultant ----- (4) Angle δ' that Resultant vector
makes with V₂ is:
We see that the denominator is 0. It means that tan δ' is infinity. Hence the angle δ' that the resultant makes with the velocity V₂ is π/2.