ACCELERATION OF A SKIER
A skier moves along a ski-jump ramp (Fig. 3.14a). The ramp is straight from point A to point C and curved from point C onward. The skier speeds up as she moves downhill from point A to point E, where her speed is maximum. She slows down after passing point E. Draw the direction of the acceleration vector at each of the points B, D, E, and F.
Figure 3.14b shows our solution. At point B the skier is moving in a straight line with increasing speed, so her acceleration points downhill, in the same direction as her velocity. At points D, E, and F the skier is moving along a curved path, so her acceleration has a component perpendicular to the path (toward the concave side of the path) at each of these points. At point D there is also an acceleration component in the direction of her motion because she is speeding up. So the acceleration vector points ahead of the normal to her path at point D. At point E, the skier’s speed is instantaneously not changing; her speed is maximum at this point, so its derivative is zero. There is therefore no parallel component of \overrightarrow{\boldsymbol{a}}, and the acceleration is perpendicular to her motion. At point F there is an acceleration component opposite to the direction of her motion because she’s slowing down. The acceleration vector therefore points behind the normal to her path.
In the next section we’ll consider the skier’s acceleration after she flies off the ramp.