JAMB Physics 2018 Paper

Concept:The eastward and northward displacements are perpendicular, so the resultant displacement can be found using Pythagoras theorem and trigonometry.Explanation:The $1$ km due east and $1$ km due north form the two shorter sides of a right-angled triangle.The displacement is the hypotenuse of this triangle.Using Pythagoras theorem:$R^2 = 1^2 + 1^2$$R^2 = 1 + 1 = 2$$R = \sqrt{2}$ km.To find the direction, use $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$$\tan \theta = \frac{1}{1} = 1$$\theta = \tan^{-1}(1) = 45^\circ$.The angle is measured from the north towards the east, so the displacement is $\sqrt{2}$ km $N45^\circ E$.Answer:$\sqrt{2}$ km $N45^\circ E$ Option A.