The correct solution to the problem is that the direction of the resultant force will be approximately 37.33° from the horizontal above the ground.
What is Vector and how do we do component of a Vector ?
- In a coordinate plane there are two axis one is x axis and the second one is y axis.
- If a vector is lying in the coordinate plane then no matter what is its direction, we can always divide it in two components which are x component and y component for easier calculations.
- If the magnitude of the vector is R, then the magnitude of the X component along x axis will be R cos θ and the magnitude of the Y component along y axis will be R sin θ.
- We can find the final resultant magnitude and direction of the vector from the components by adding the the components.
How to solve this question ?
For 30° Vector of 40 pounds :-
If we divide it in components it will become
40 cos 30° Î + 40 sin 30° Ĵ
40 × ( √3 / 2 ) Î + 40 × ( 1 / 2 ) Ĵ
34.64 Î + 20 Ĵ ( approximately )
For 45° Vector of 35 pounds :-
If we divide it in components it will become
35 cos 45° Î + 35 sin 45° Ĵ
35 × ( 1 / √2 ) Î + 35 × ( 1 / √2 ) Ĵ
24.75 Î + 24.75 Ĵ ( approximately )
Now adding both vectors
( 24.75 + 34.64 ) Î + ( 24.75 + 20 ) Ĵ ( approximately )
59.39 Î + 44.74 Ĵ ( approximately )
Now Using formula of Tan θ to find the value of θ
( Tan θ = Perpendicular / Base )
Tan θ = 44.74 / 59.39
Tan θ = 0.75 ( approximately )
θ = Tan⁻¹ (0.75) ( approximately )
θ = 36.87° ( approximately )
We are calculated the value of θ as 36.87° which is approximate value as we used a lot of approximations while calculating and, the closest option given is 37.33° which is again an approximate value.
So we can say that the correct answer to this problem is The direction of the resultant force will be approximately 37.33° from the horizontal above the ground.
Learn more about Vectors here:
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