Chapter 27

A force of \(4 \mathrm{~N}\) is inclined at an angle of \(45^{\circ}\) to a second force of \(7 \mathrm{~N}\), both forces acting at a point. Find the magnitude of the resultant of these two forces and the direction of the resultant with respect to the \(7 \mathrm{~N}\) force by both the 'triangle' and the 'parallelogram' methods.

Resolve the acceleration vector of \(17 \mathrm{~m} / \mathrm{s}^{2}\) at an angle of \(120^{\circ}\) to the horizontal into a horizontal and a vertical component.

Accelerations of \(a_{1}=1.5 \mathrm{~m} / \mathrm{s}^{2}\) at \(90^{\circ}\) and \(a_{2}=2.6 \mathrm{~m} / \mathrm{s}^{2}\) at \(145^{\circ}\) act at a point. Find \(a_{1}+a_{2}\) and \(a_{1}-a_{2}\) by (i) drawing a scale vector diagram and (ii) by calculation.

Calculate the resultant of (i) \(v_{1}-v_{2}+v_{3}\) and (ii) \(v_{2}-v_{1}-v_{3}\) when \(v_{1}=22\) units at \(140^{\circ}, v_{2}=40\) units at \(190^{\circ}\) and \(v_{3}=15\) units at \(290^{\circ}\)

Two cars, \(P\) and \(Q\), are travelling towards the junction of two roads which are at right angles to one another. Car \(P\) has a velocity of \(45 \mathrm{~km} / \mathrm{h}\) due east and car \(Q\) a velocity of \(55 \mathrm{~km} / \mathrm{h}\) due south. Calculate (i) the velocity of car \(P\) relative to \(\operatorname{car} Q\), and (ii) the velocity of car \(Q\) relative to car \(P\).