First slide

Vectors

Question

A car going due North at 10 $\sqrt{2}$ ${ms}^{- 1}$ turns right through an angle of $90^{0}$ without changing speed. The change in velocity of car is

Moderate

A

20 ${ms}^{- 1}$ in South-East direction
B

$20 \sqrt{2} {ms}^{- 1}$ in South-East direction
C

20 ${ms}^{- 1}$ North-East direction
D

20 ${ms}^{- 1}$ in North-West direction

Solution

Initial velocity is $v_{i} = 10 \sqrt{2} \hat{j}$
Final velocity is $∆ v = v_{f} - v_{i} = 10 \sqrt{2} i - 10 \sqrt{2} \hat{j}$
$∴ The change in velocity is$

$∆ v = v_{f} - v_{i} = 10 \sqrt{2} i - 10 \sqrt{2} \hat{j}$
$∴ | ∆ v | = \sqrt{{(10 \sqrt{2})}^{2} + {(10 \sqrt{2})}^{2}} = \sqrt{400}$
= $20 {ms}^{- 1} in South - East direction$

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