Mosquitoes in the circle

Classical Mechanics Level 2

Find the magnitude of the resultant of the three vectors O A → , O B → , O C → \overrightarrow { OA } ,\overrightarrow { OB } ,\overrightarrow { OC } as shown in the figure. Radius of the circle is R.

R R 2 R\sqrt { 2 } R ( 1 + 2 ) R\left( 1+\sqrt { 2 } \right) R 2 \frac { R }{ \sqrt { 2 } }

Dinesh Nath Goswami by Dinesh Nath Goswami , 20, India

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1 solution

Resolve along OB. OC * Cos45 + OB + OA * Cos45=R * Cos45 + R + R * Cos45
= R ( 1 + 2 ∗ s q r t 2 ∗ 2 ) R e s o l v e ⊥ O B . O C ∗ C o s 45 u p + O A ∗ C o s 45 d o w n = 0. ∴ R e s u l t a n t = R ( 1 + 2 ∗ s q r t 2 ∗ 2 ) = R ( 1 + s q r t 2 ) =R(1+2*sqrt 2 *2)\\Resolve \perp OB. ~~OC * Cos45 up + OA * Cos45 down =0.\\\therefore~Resultant =R(1+2*sqrt 2 *2)=R(1+sqrt 2)

3 Helpful 0 Interesting 0 Brilliant 0 Confused

absolutely correct. nice solution:)

Dinesh Nath Goswami - 5 years, 12 months ago

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