A skateboarder travels on a horizontal surface with an initial velocity of 4.0 m/s toward the south and a constant acceleration of 1.8 m/s2 toward the east. Let the x direction be eastward and the y direction be northward, and let the skateboarder be at the origin at t=0.

a)What is her x position at t=0.60s?

b)What is her y position at t=0.60s?

c)What is her x velocity component at t=0.60s?

d)What is her y velocity component at t=0.60s?

a) 0.32 m b) -2.4 m c) 1.08 m/s d) -4 m/s

Explanation:

a)

As the x and y axes (as chosen) are perpendicular each other, the movements along these axes are independent each other.This means that we can use the kinematic equations for displacements along both axes.In the x direction, as the only initial velocity is in the south direction (-y axis), the skateboarder is at rest, so we can write:

       

In the y-direction, as no acceleration is acting on the skateboarder, we can write  the following displacement equation:

       

For t = 0.6s, replacing by the givens, we get the position (displacement from the origin) on the x-axis, as follows:

       

b)

From (2) we can get the position on the y-axis (displacement from the origin) as follows:

       

c)

In the x- direction, we can find the component of the velocity along this direction, as follows:

       

Replacing by the values, we have:

       

d)

As the skateboarder moves along the y-axis at a constant speed equal to her initial velocity, we  have:

        vfy = voy = -4 m/s