A particle moves in x - y plane. The position vector of the particle at any time t is r → = 2 t i ^ + 2 t 2 j ^ m . The rate of change of θ at time t = 2 s (where θ is the angle which its velocity vector makes with positive x -axis ) is

Question

A particle moves in x - y plane. The position vector of the particle at any time t is r → = 2 t i ^ + 2 t 2 j ^ m . The rate of change of θ at time t = 2 s (where θ is the angle which its velocity vector makes with positive x -axis ) is, 2 17 r a d s - 1, 1 14 r a d s - 1, 4 7 r a d s - 1, 6 5 r a d s - 1

MARKS App · Accepted Answer

x = 2 t ⇒ v x = d x d t = 2 y = 2 t 2 ⇒ v y = d y d t = 4 t ∴ tan ⁡ θ = v y v x = 4 t 2 = 2 t Differentiating with respect to time we get, sec 2 ⁡ θ d θ d t = 2 or 1 + tan 2 ⁡ θ d θ d t = 2 or 1 + 4 t 2 d θ d t = 2 or d θ d t = 2 1 + 4 t 2 d θ d t a t t = 2 s i s d θ d t = 2 1 + 4 2 2 = 2 17 r a d s - 1

Search any question & find its solution

Looking for more such questions to practice?