First slide

Scalars and Vectors

Question

A particle travels with speed 50 m/s from the point (3 m, -7 m) in a direction $7 \hat{i} - 24 \hat{j}$ . Find its position vector after 3 seconds.

Moderate

A

$(45 \hat{i} - 125 \hat{j}) m$
B

$(45 \hat{i} - 151 \hat{j}) m$
C

$(45 \hat{i} + 125 \hat{j}) m$
D

$(35 \hat{i} - 115 \hat{j}) m$

Solution

$Given speed v = 50 m / s in the direction \vec{a} = 7 \hat{i} - 24 \hat{j}$
$\vec{v} = v \hat{a}; \hat{a} is the unit vector in the direction 7 \hat{i} - 24 \hat{j}$
$\begin{array}{l} \hat{a} = \frac{(7 \hat{i} - 24 \hat{j})}{\sqrt{(24)^{2} + (7)^{2}}} = \frac{(7 \hat{i} - 24 \hat{j})}{25} \\ \vec{v} = v \hat{a} = 50 \cdot \frac{(7 \hat{i} - 24 \hat{j})}{25} = 2 (7 \hat{i} - 24 \hat{j}) m / s \end{array}$
$Initially the particle is at {\vec{r}}_{0} = (3 \hat{i} - 7 \hat{j}) m$
$Position of the particle after 3 \sec, \vec{r} = {\vec{r}}_{0} + \vec{v} t$
$\Rightarrow \vec{r} = (3 \hat{i} - 7 \hat{j}) + 3 \times 2 (7 \hat{i} - 24 \hat{j}) = (45 \hat{i} - 151 \hat{j}) m$

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