Newton's 2nd Law relates the net force <em>F</em> on an object of mass <em>m </em>with the acceleration <em>a</em> it experiments by <em>F=ma.</em> In our case the net force is the friction force, since it's the only one the skier is experimenting horizontally and the vertical ones cancel out since he's not moving in that direction. Our acceleration then will be:
Also, acceleration is defined by the change of velocity in a given time t, so we have:
Since we want the change in velocity, <em>mixing both equations</em> we conclude that:
The weight is acting downwards where as the buoyant force acting upwards (opposite) direction with equal amount of force. so the opposite forces cancel out each other (because of the force amount being equal) and no net force is acting on the object.
The orbital speeds of stars far from the galactic center are surprisingly high, suggesting that these stars are feeling gravitational effects from unseen matter in the halo.