A vector makes an angle, theta, with the horizontal. The horizontal and vertical components of the vector will be equal in magni
2 answers:
Answer:
The correct option is;
c. 45°
Explanation:
The given information is that the angle the vector makes with the horizontal = θ
Let the magnitude of the resultant vector = R
The horizontal component of the vector are given as follows;
Rₓ = R × cos(θ)
The vertical component of the vector are given as follows;
= R × sin(θ)
The resultant vector, R, in vector form, R, is the sum of the horizontal and vertical components as follows;
R = R × cos(θ)·i + R × sin(θ)·j
Therefore;
The horizontal and vertical component will be equal when cos(θ) = sin(θ)
Given that tan(θ) = sin(θ)/cos(θ), we have that when cos(θ) = sin(θ), tan(θ) = sin(θ)/cos(θ) = sin(θ)/sin(θ) = 1
tan(θ) = 1,
∴ θ = tan⁻¹(1) = 45°
θ = 45°.
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