Two forces P and Q whose resultant is 10Newtons are at right angles to each other. If P makes 30 degrees with the resultant, determine the magnitude of Q in Newton.

Q=10sin30=5

To solve this problem, we can use vector addition and trigonometric functions. Here's how:

1. Draw a diagram: Draw the two forces, P and Q, at right angles to each other, and label the resultant as R.

2. Find the magnitude of P: Since the resultant is 10 Newtons, and P makes an angle of 30 degrees with the resultant, we can use trigonometry to find the magnitude of P. The magnitude of P can be found using the formula: P = R * cos(theta), where theta is the angle between P and R.

P = 10 Newtons * cos(30 degrees)
P = 10 Newtons * (√3/2)
P ≈ 8.66 Newtons

3. Find the magnitude of Q: To find the magnitude of Q, we can use the Pythagorean theorem because P and Q form a right triangle with the resultant R as the hypotenuse. The Pythagorean theorem states that the square of the hypotenuse (R) is equal to the sum of the squares of the other two sides (P and Q).

R^2 = P^2 + Q^2
Q^2 = R^2 - P^2

Since we know R = 10 Newtons and P ≈ 8.66 Newtons, we can substitute these values into the equation to solve for Q.

Q^2 = (10 Newtons)^2 - (8.66 Newtons)^2
Q^2 = 100 Newtons^2 - 75.03 Newtons^2
Q^2 ≈ 24.97 Newtons^2

Taking the square root of both sides gives us the magnitude of Q:

Q ≈ √24.97 Newtons
Q ≈ 4.997 Newtons

Therefore, the magnitude of Q is approximately 4.997 Newtons.