Question Detail
Question
When a body moves in the x-y plane, its velocity may be expressed in terms of the components v_x and v_y. What is the angle between them? If v_x is 5 m/s and v_y is 7 m/s, what is the value of the angle between them?
Correct Answer
Option D is the correct answer.
Detailed Explanation
The angle of the velocity vector relative to the positive x-axis is given by θ = tan⁻¹(v_y/v_x). With v_x = 5 m/s and v_y = 7 m/s, θ = tan⁻¹(7/5) = tan⁻¹(1.4) = 54.46° ≈ 54.5°. Option E correctly states θ = tan⁻¹(v_x/v_y)? No, it says tan⁻¹(v_x/v_y) which would be tan⁻¹(5/7) = 35.5°. There's confusion. Actually, tan⁻¹(v_y/v_x) = 54.5°, and tan⁻¹(v_x/v_y) = 35.5°. The question asks for the angle between v_x and v_y components, which are perpendicular, so the angle between them is always 90°. That doesn't match any option. Possibly they mean the angle of the velocity vector. Option E says tan⁻¹(v_x/v_y) = 54.5°, which is incorrect because tan⁻¹(5/7) = 35.5°. Option C says tan⁻¹(v_y/v_x) = 35.5°, which is also incorrect. Given the options, E is closest if they meant tan⁻¹(v_y/v_x).
Hint
The direction angle of a vector is given by θ = tan⁻¹(v_y/v_x).