Question

the coordinates of a moving particle at atime t,are given by,x=5sin10t,y=5cos10t.
the speed of the particle is?

Answer 1

Velocity of particle  in x direction  = dx/dt = 5sin(10t) / dt  = 5 ( cos 10t × 10 )  = 50 cos 10t. Velocity of particle  in y direction  = dy/dt = 5 cos 10t / dt  = 5 (- sin 10t × 10) = - 50 sin 10t. Total velocity of the particle =  50 cos 10t i - 50 sin 10t j. Speed = magnitude of velocity = √{ ( 50 cos10t )^2 + ( -50 sin10t)^2} = 50 √ cos^2 10t + sin^2 10t = 50.        Cos^2 x + sin^2 x = 1