Two forces P and Q acts on a hook as shown.             Given: P = 100 N; θ1 = 19°If the resultant force is 210 N acting downwards to the right at an angle of 20° with the horizontal, what is the value of ? in N?QUESTION 9ANSWERA.165.4B.146.5C.154.6D.164.5

The problem involves two forces, P and Q, and their resultant force. We know the magnitude and direction of P and the resultant force, and we need to find the magnitude of Q.

Here are the steps to solve the problem:

1. First, we need to resolve the forces into their horizontal and vertical components. The horizontal component (H) and vertical component (V) of a force can be calculated using the equations H = Fcosθ and V = Fsinθ, where F is the magnitude of the force and θ is the angle it makes with the horizontal.

2. The horizontal component of P is Pcosθ1 = 100cos19° = 94.5 N (to the right), and the vertical component is Psinθ1 = 100sin19° = 32.4 N (upwards).

3. The resultant force also has horizontal and vertical components. The horizontal component is 210cos20° = 197.4 N (to the right), and the vertical component is 210sin20° = 71.7 N (downwards).

4. The horizontal component of the resultant force is the sum of the horizontal components of P and Q, and the vertical component of the resultant force is the sum of the vertical components of P and Q. Therefore, the horizontal component of Q is 197.4 - 94.5 = 102.9 N (to the right), and the vertical component of Q is 71.7 + 32.4 = 104.1 N (downwards).

5. Finally, we can find the magnitude of Q using the Pythagorean theorem: Q = sqrt((horizontal component)^2 + (vertical component)^2) = sqrt((102.9)^2 + (104.1)^2) = 146.5 N.

So, the answer is B. 146.5 N.