First slide

Projection Under uniform Acceleration

Question

A particle staring from the origin (0, 0) moves in a straight line in the (x,y) plane. Its coordinates at a later time are ( $\sqrt{3}$ , 3 ). The path of the particle makes with the x-axis an angle of:

Moderate

A

$30^{0}$
B

$45^{0}$
C

$60^{0}$
D

$0^{0}$

Solution

Slope of the path of the particle gives the measure of angle required.
Draw the situation as shown. OA represents the path of the particle starting from origin O (0,0). Draw a perpendicular from point A to x-axis. Let path of the particle makes an angle $θ$ with the x-axis, then
$\tan θ = slope of line OA = \frac{AB}{OB} = \frac{3}{\sqrt{3}} = \sqrt{3}$
or $θ = 60^{0}$

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