Bearing and compass direction problems

3 \includegraphics[max width=\textwidth, alt={}, center]{4b703cf9-b3d3-4210-b57b-89136595f8a5-02_570_495_1114_826} Three horizontal forces of magnitudes \(12 \mathrm {~N} , 5 \mathrm {~N}\), and 9 N act along bearings \(000 ^ { \circ } , 150 ^ { \circ }\) and \(270 ^ { \circ }\) respectively (see diagram).

1. Show that the component of the resultant of the three forces along bearing \(270 ^ { \circ }\) has magnitude 6.5 N .
2. Find the component of the resultant of the three forces along bearing \(000 ^ { \circ }\).
3. Hence find the magnitude and bearing of the resultant of the three forces.

1 Three horizontal forces, acting at a single point, have magnitudes \(12 \mathrm {~N} , 14 \mathrm {~N}\) and 5 N and act along bearings \(000 ^ { \circ } , 090 ^ { \circ }\) and \(270 ^ { \circ }\) respectively. Find the magnitude and bearing of their resultant.

2 \includegraphics[max width=\textwidth, alt={}, center]{66eb8290-3a80-40bf-be40-a936ed7d5a1b-2_309_520_941_744} A particle rests on a smooth horizontal surface. Three horizontal forces of magnitudes \(2.5 \mathrm {~N} , F \mathrm {~N}\) and 2.4 N act on the particle on bearings \(\theta ^ { \circ } , 180 ^ { \circ }\) and \(270 ^ { \circ }\) respectively (see diagram). The particle is in equilibrium.

1. Find \(\theta\) and \(F\). The 2.4 N force suddenly ceases to act on the particle, which has mass 0.2 kg .
2. Find the magnitude and direction of the acceleration of the particle.

Two forces \(\mathbf{F_1}\) and \(\mathbf{F_2}\) act on a particle. The force \(\mathbf{F_1}\) has magnitude 8 N and acts due east. The resultant of \(\mathbf{F_1}\) and \(\mathbf{F_2}\) is a force of magnitude 14 N acting in a direction whose bearing is \(120°\). Find

1. the magnitude of \(\mathbf{F_2}\), [4]
2. the direction of \(\mathbf{F_2}\), giving your answer as a bearing to the nearest degree. [5]

Forces of magnitude \(4\) N, \(5\) N and \(8\) N act on a particle in directions whose bearings are \(000°\), \(090°\) and \(210°\) respectively. Find the magnitude of the resultant force and the bearing of the direction in which it acts. [7 marks] \includegraphics{figure_2}

Two forces, both of magnitude 5 N, act on a particle in the directions with bearings 000° and 070°, as shown. \includegraphics{figure_1} Calculate

1. the magnitude of the resultant force on the particle, [3 marks]
2. the bearing on which this resultant force acts. [2 marks]