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.

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Solution

(b) 70 km/h towards south-west Final velocity, $\stackrel{\to }{{V}_{f}}=-50\stackrel{^}{i}\mathrm{km}/\mathrm{h}$ Initial velocity, $\stackrel{\to }{{V}_{i}}=50\stackrel{^}{j}\mathrm{km}/\mathrm{h}$ Change in velocity, $∆\stackrel{\to }{V}=\stackrel{\to }{{V}_{f}}-\stackrel{\to }{{V}_{i}}$ $\left|∆V\right|=\sqrt{{50}^{2}+{50}^{2}+2×50×50\mathrm{cos}\left(90°\right)}=70\mathrm{km}/\mathrm{h}$ It is towards southwest, as shown in the figure.

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