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Question

A bird is flying due east with a velocity of 4 m/s. The wind starts to blow with a velocity of 3 m/s due north. What is the magnitude of relative velocity of bird w.r.t. wind? Find out the angle it makes with the x-axis?


A

7m/s,tan1(34)

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B

7 m/s, tan1(43)

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C

5 m/s, tan1(34)

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D

5 m/s,tan1(43)

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Solution

The correct option is C

5 m/s, tan1(34)


Method - 1:

Whenever two bodies are moving at right angle to each other,

then their relative velocity is obtained by taking square root of

the sum of square root of the sum of squares of respective velocities.

Here Velocity of bird = VB=4ms1 towards east.

Velocity of wind = vw=3ms1 towards north, Velocity of bird

w.r.t wind = vbw=?

vb,w=vbvw=vb+(vw)

So,vb,w=vb2+vw2=(3)2+(4)2=25=5ms1

To find direction we need to find angle β is angle between relative velocity and velocity of bird.

tan β=3 sin904+3 cos 90=34

[=90, angle between them w.r.t east i.e., vb and vw].B = tan1(34)

Method - 2:

vb,w=vbvw=vb+(vw)=4^i+(3^j)(ms)=4^i3^j(m/s)

|vb,w|=(4)2+(3)2=5m/s

Here the direction of the relative velocity of the bird is |tanβ|=34β=

tan1(34)

Here the relative velocity of the bird with respect to wind is 5 m/s and in the direction tan1(34) from east towards south.


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