Answer:
Part a)
Part b)
Part c)
Explanation:
Part a)
As we know that the gravitational force is given as
so we will have to find the ratio of force on two planets due to star
so here we have
Part b)
Orbital speed is given as
so the ratio of two orbital speed is given as
Part c)
Time period is given as
so the ratio of two time period is given as
Answer:
68.8 N 13.8°N of W
Explanation:
F₁ is 50 N 30°N of W. The terminal angle is 150°.
F₂ is 25 N 20°S of W. The terminal angle is -160°.
Graphically, you can add the vectors using head-to-tail method. Move F₂ so that the tail of the vector is at the head of F₁. The resultant vector will be from the tail of F₁ to the head of F₂.
Algebraically, find the x and y components of each vector.
F₁ₓ = 50 N cos(150°) = -43.3 N
F₁ᵧ = 50 N sin(150°) = 25 N
F₂ₓ = 25 N cos(-160°) = -23.5 N
F₂ᵧ = 25 N sin(-160°) = -8.6 N
The x and y components of the resultant vector are the sums:
Fₓ = -43.3 N + -23.5 N = -66.8 N
Fᵧ = 25 N + -8.6 N = 16.4 N
The magnitude of the resultant force is:
F = √(Fₓ² + Fᵧ²)
F = √((-66.8 N)² + (16.4 N)²)
F = 68.8 N
The direction of the resultant force is:
θ = tan⁻¹(Fᵧ / Fₓ)
θ = tan⁻¹(16.4 N / -66.8 N)
θ = 166.2°
θ = 13.8°N of W
