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Integration of Irrational Algebraic Fractions - 2

The co-ordina...

Question

The co-ordinates of a moving particle at a time $t$ , are given by $x = 5 s i n 10 t, y = 5 c o s 10 t$ . The speed of the particle is

A

25

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B

50

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C

10

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D

50 \sqrt{2}

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Solution

The correct option is B $50$
$v_{x} = \frac{d x}{d t} = 50 c o s 10 t,$
$v_{y} = \frac{d y}{d t} = - 50 s i n 10 t$
Speed $= \sqrt{v_{x}^{2} + v_{y}^{2}}$
$= \sqrt{(50 c o s 10 t)^{2} + (- 50 s i n 10 t)^{2}} = 50$

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