The box slides down the slope described by the equation y = 0.05x^2 m , where x is in meters. If the box has components of velocity and acceleration of vx = 3 m/s and ax = -1.5 m/s^2 at x = 5 m determine the y component of the velocity and acceleration
The answers to the question were 3 m/s and 0.15 m/s^2 respectively. Getting the velocity was easy enough but I'm not sure how to get acceleration. I'm hoping some of you may be able to help.
The Attempt at a Solution
Getting velocity was simply done by taking the derivative of the slope (dy/dx = 0.1x). At x = 5 the slope is 0.5 so the y component of velocity is equal to vy = vx * 0.5 = 1.5 m/s
In terms of getting acceleration there are two components one parallel to the motion and one perpendicular. There is no indication of how the velocity is changing so I know of no of getting the tangential component.
My first attempt was find an acceleration vector such that is perpendicular to the motion (that is wrong because the path is a parabola). My second attempt was to use dynamics at that particular point to determine the y component of acceleration (assuming that gravity had something to do with it). Again, my answer was wrong.
I would be grateful for an explanation as to how to get to the answer 0.15 m/s^2 for the y-component of acceleration.