Question

A motor car is going due north at a speed of 50 km/h. It makes a 90° left turn without changing the speed. The change in the velocity of the car is about
(a) 50 km/h towards west
(b) 70 km/h towards south-west
(c) 70 km/h towards north-west
(d) zero.

Answer 1

(b) 70 km/h towards south-west

Final velocity, $\overrightarrow{V_f}=-50\hat{i}\mathrm{km}/\mathrm{h}$
Initial velocity, $\overrightarrow{V_i}=50\hat{j}\mathrm{km}/\mathrm{h}$
Change in velocity, $∆\overrightarrow{V}=\overrightarrow{V_f}-\overrightarrow{V_i}$
$\left|∆V\right|=\sqrt{{50}^2+{50}^2+2\times 50\times 50\cos \left(90°\right)}=70\mathrm{km}/\mathrm{h}$
It is towards southwest, as shown in the figure.