A particle is projected with initial velocity 50m/sec making an angle of 53° with horizontal. Find the radius of curvature of particle when velocity of particle is perpendicular to the direction of its initial velocity :
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Question

A particle is projected with initial velocity 50m/sec making an angle of 53° with horizontal. Find the radius of curvature of particle when velocity of particle is perpendicular to the direction of its initial velocity :

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G1 Physics · Accepted Answer

Take sin53°=0.8, cos53°=0.6, so u⃗=(30î+40ĵ) m/s. When v⃗·u⃗=0, 30(30)+40(40-10t)=0, giving t=6.25 s and v=37.5 m/s. The normal component of g is g cos36.87°=8 m/s², so ρ=v²/aₙ=37.5²/8≈175.8 m. Hence A.