Answer:
α = 60 degr
Step-by-step explanation:
To find the magnitude and direction of the resultant force, we can use the law of cosines and the law of sines:
Magnitude:
Let's call the forces A = 10N and B = 20N. The angle between them is 60 degrees. The magnitude of the resultant force R can be found using the formula:
R² = A² + B² - 2AB cosθ
where θ is the angle between the forces. Substituting the values we get:
R² = (10N)² + (20N)² - 2(10N)(20N) cos(60)
R² = 100N² + 400N² - 200N²
R² = 300N²
Taking the square root of both sides, we get:
R = sqrt(300N²) = 10 sqrt(3) N
Therefore, the magnitude of the resultant force is 10 sqrt(3) N.
Direction:
The direction of the resultant force can be found using the law of sines. Let's call the angle between the resultant force and the 10N force α, and the angle between the resultant force and the 20N force β. Then we have:
sin α / R = sin β / B
Substituting the values we get:
sin α / (10 sqrt(3) N) = sin 60 / 20N
Simplifying, we get:
sin α = (10 sqrt(3) N / 20N) sin 60
sin α = sqrt(3) / 2
Taking the inverse sine of both sides, we get:
α = 60 degrees
Therefore, the direction of the resultant force is 60 degrees from the 10N force