A particle is moving in xy-plane with a constant speed v 0 such that its y displacement is given by y = α e - 2 v x 3 v 0 , where v x is component of velocity along the x-axis. If at some instant x component of it velocity is positive and the slope of the tangent on its path is - 1 3 , then the displacement of the particle in y-direction at the instant is

Step-by-step solution

Here, particle is moving in two - dimensional (x – y) plane, with constant speed so slope of graph d y d x = v y v x and v 0 = v x 2 + v y 2 . As slope, dy dx = - 1 3 = v y v x So, v x = - v y 3 On squaring and adding v x 2 + v y 2 = v 0 2 3 v y 2 + v y 2 = v 0 2 v y = ± v 0 2 v x = ∓ 3 v 0 2 So, y = α e - 2 3 v 0 × 3 v 0 2 y = α e - 1