4.22 and are unit vectors along x- and y- axis respectively. What is the magnitude and direction of the vectors + , and - ? What are the components of a vector A= 2 + 3 along the directions of + , and - ? [You may use graphical method]
4.22 and are unit vectors along x- and y- axis respectively. What is the magnitude and direction of the vectors + , and - ? What are the components of a vector A= 2 + 3 along the directions of + , and - ? [You may use graphical method]
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1 Answer
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4.22
Let us consider a vector . The equation can be written as
Px = Py = 1 = = = …….(i)
So the magnitude of vector + =
Let be the angle made by vector , with the x axis as given in the above figure
= = , = 45 with the x axis
Let = -
– = ( –
= = 1
= =
Hence = . Therefore the magnitude of ( + =
Let
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Please find the solution below:
after 10 kicks,
v? = 3tî v? = 24cos 60°î + 24sin 60°? = 12î + 12√3?
v? = v? – v? = (12 – 3t)î + 12√3?
It is minimum when 12 - 3t = 0 ⇒ t = 4sec
ω = θ² + 2θ
α = (ωdω)/dθ = (θ² + 2θ) (2θ + 2)
At θ = 1rad.
ω = 3rad/s and α = 12rad/s²
a? = αR = 12 m/s² a? = ω²R = 9 m/s² A? = √ (a? ² + a? ²) = 15 m/s²
a? = v? ²/4r
a_A? = (v? ²/r²) × r = v? ²/r
a_A = 3v? ²/4r
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