Two forces whose
resultants is 100N are
perpendicular to each
other. If one of them
makes an angle of 60
degree with the
horinzontal. Calculate its
magnitude
Not enough information. The direction of one of the vectors is not enough. We know that the other is perpendicular to it, and that the diagonal of the rectangle is 100. But that just means that the rectangle is rotated by 60°
It could have sides of 60 and 80, or 12 and 8√154, or any other shape.
Asking
To calculate the magnitude of the force, we can use trigonometry. Since one of the forces makes an angle of 60 degrees with the horizontal, we can consider this force as the hypotenuse of a right triangle. The other force will be one of the sides of the right triangle.
Let's denote the magnitude of the force that makes an angle of 60 degrees as F₁ and the magnitude of the other force as F₂.
According to the problem, the resultant force (hypotenuse) is 100N. So, we have:
F₁² + F₂² = 100²
Since the forces are perpendicular to each other, we can use trigonometric functions to relate F₁ and F₂. The sine function relates the opposite side (F₁) to the hypotenuse (100N):
sin(60) = F₁ / 100
To solve for F₁, we can rearrange the equation:
F₁ = sin(60) * 100
Using a calculator, we find:
F₁ ≈ 86.6N
Therefore, the magnitude of the force that makes an angle of 60 degrees with the horizontal is approximately 86.6N.