Resolve a displacement of 700 cm into two components along direction lines that lie on opposite sides of the displacement and each of which makes an angle of 30° with the displacement.
404 cm and 478 cm
404 cm each
383 cm and 415 cm
415 cm each
To resolve a displacement into two components along direction lines that make an angle with the displacement, you can use trigonometry. In this case, the angle is given as 30°.
Let's denote the displacement as D and the components as C1 and C2.
We can start by finding the magnitude of the components. Since the angle between the displacement and each component is 30°, we can use the cosine function to find the magnitude of each component.
cos(30°) = adjacent/hypotenuse
Since the adjacent side is the magnitude of each component and the hypotenuse is the magnitude of the displacement, we have:
cos(30°) = C1/D
cos(30°) = C2/D
Now we can solve for C1 and C2 by rearranging the equations:
C1 = D * cos(30°)
C2 = D * cos(30°)
Given that the displacement D is 700 cm, we can substitute this value into the equations:
C1 = 700 cm * cos(30°) ≈ 700 cm * 0.866 ≈ 606.2 cm ≈ 606 cm (rounded to the nearest whole number)
C2 = 700 cm * cos(30°) ≈ 700 cm * 0.866 ≈ 606.2 cm ≈ 606 cm (rounded to the nearest whole number)
Thus, the correct answer is 606 cm and 606 cm.