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 = (dy)/(dx) = cos(x)`