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A particle has two velocity v1 andv2 .its resultant velocity is equal to v1 in magnitude. Find the angle which the new resultant makes with v2 when v1 is doubled. |
| Answer» DIAGRAM for the way vectors are added and the angle that resultant makes.Resultant vector with an angle Ф between them is GIVEN by the law of vector addition : V² = V₁² + V₂² + 2 V₁ V₂ Cos Ф --- (1) = V₁² given=> V₂ = - 2 V₁ Cos Ф ---- (2) Angle δ between the resultant vector V and V₂ is given by : ----- (3)=============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: ----- (5) 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. | |