# 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.

2
by Arundhuti

• Brainly User
2015-04-23T16:54:03+05:30
Let the magnitudes of velocities be respectively.
And the angle between them be .
From the data provided,
.
Now, the angle made by new resultant with when is doubled is,
Since denominator is 0, angle made by resultant is 90°.
2015-04-23T21:21:00+05:30

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See the 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.