Question

Find the rectangular components of a velocity of 8 m
s-1 when one of the components makes an angle of
30° with the resultant.​

Answer 1

Answer:

X component = 4√3 or 6.92 m/s

Y component = 4 m/s

Explanation:

By Resolution of Vectors,

X component : Resultant × Cos30° = 8 × √3/2 = 4√3 or 6.92 (√3 = 1.73) m/s

Y component : Resultant × Sin30° = 8 × 1/2 = 4 m/s.

I hope it helped!!

Answer 2

Answer:

The rectangular components of given velocity are $4m/s$ and $4\sqrt{3}$.

Explanation:

Given that,

Velocity of body=8m/s

We are required to find the rectangular components of this velocity if one of the component makes an angle $\theta=30$ with resultant.

If any vector makes an angle $\theta$ with other vector,its magnitude is cosine of the angle made to the magnitude of other vector.Therefore,

One of the rectangular components is

$8cos30^{0}=8\times\frac{\sqrt{3} }{2} =4\sqrt{3}m/s$

As one component makes an angle of 30* with resultant,the other makes

$90-30=60^{0}$ with the resultant.Therefore,

Other rectangular component is

$8sin30^{0}=8\times\frac{1 }{2} =4m/s$

Hence the rectangular components of given velocity are $4m/s$ and $4\sqrt{3}$.

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