Question

kindly solve it out....

Answer 1

let initial position of particle = R i
final position of particle = Rcos∅i + Rsin∅ j

so, displacement of particle = final position - initial position
= Rcos∅i + Rsin∅ j - Ri
=( 1+ cos∅) R i + Rsin∅ j

magnitude =√{( 1+cos∅)²R²+ (sin∅)²R²}
= R√{ 1 + 2cos∅ +cos²∅ + sin²∅}
=R√{ 1+ 2cos∅ + 1 } [ cos²x + sin²x = 1 use
=R√{2(1+cos∅)
=R√2×2sin²∅/2 [ use (1+cos∅ = 2sin²∅/2
=2Rsin∅/2 ( answer )