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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 ______.
Options
50 km/h towards west
70 km/h towards south-west
70 km/h towards north-west
zero
Solution
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 70 km/h towards south-west.
Explanation:
Final velocity, \[\vec{V_f} = - 50 \hat{ i } \text{ km } /\text{ h } \] Initial velocity, \[\vec{V_f} = - 50 \hat{ i } \text{ km } /\text{ h } \] Change in velocity, \[∆ \vec{V} = \vec{V_f} - \vec{V_i}\] \[\left| ∆ V \right| = \sqrt{{50}^2 + {50}^2 + 2 \times 50 \times 50\cos\left( 90° \right)} = 70 \text{ km } /h\]
It is towards the southwest, as shown in the figure.
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