Question

The motorcycle travels with a constant speed v0 along the path that, for a short distance, takes the form of a sine curve. Determine the x and y components of its velocity at any instant on the curve.

Answer 1

Let at any instant of time the speed is vo and the angle made by the bike with the horizontal is given

now we have

component of speed in x direction given as

$v_x = v_0cos\theta$

component of speed in y direction will be

$v_y = v_0sin\theta$

now from above two equations we can say that here

$\theta$ = angle with the horizontal at any instant

and since here it is a sine curve so we know that

$y = sin(x)$

so we have slope of graph

$tan\theta = \frac{dy}{dx} = cos(x)$