First slide

Vectors

Question

A scooter going due east at 10 ${ms}^{- 1}$ turns right through an angle of $90^{0}$ . If the speed of the scooter remains unchanged in taking turn, the change in the velocity of the scooter is

Moderate

A

20.0 ${ms}^{- 1}$ south-east direction
B

zero
C

10.0 ${ms}^{- 1}$ in south direction
D

14.14 ${ms}^{- 1}$

Solution

If the magnitude of vector remains same, only direction change by $θ$ then
$\vec{Δv} = \vec{v_{2}} - \vec{v_{1},}$
$\vec{Δv} = \vec{v_{2}} + (- \vec{v_{1}})$
Magnitude of change in vector $| \vec{Δv} | = 2 vsin (\frac{θ}{2})$
$| \vec{Δv} | = 2 \times 10 \times \sin (\frac{90^{0}}{2}) = 10 \sqrt{2} = 14 .14 m / s$
Direction is south-west as shown in figure.

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