A snow skier must navigate sinusoidal moguls while downhill skiing, as shown in Fig. P8.9. The...

 

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A snow skier must navigate sinusoidal moguls while downhill skiing, as shown in Fig. P8.9. The vertical position of the skier's knees is described by the equation y(t) = 12 - 12 cos(5t), where t is in seconds and y(t) is in inches. Figure P8.9 Snow skier navigating sinusoidal moguls. (a) Determine the velocity v(t) = dy/dt. (b) Determine the acceleration a(t) = dv/dt. (c) Determine the first two nonzero values of the position and accelera- tion at the time(s) when the velocity is zero. (d) Use your results of part (c) to sketch one period of the position y(t). Clearly indicate the location and magnitude of the maximum value of y(t). A snow skier must navigate sinusoidal moguls while downhill skiing, as shown in Fig. P8.9. The vertical position of the skier's knees is described by the equation y(t) = 12 - 12 cos(5t), where t is in seconds and y(t) is in inches. Figure P8.9 Snow skier navigating sinusoidal moguls. (a) Determine the velocity v(t) = dy/dt. (b) Determine the acceleration a(t) = dv/dt. (c) Determine the first two nonzero values of the position and accelera- tion at the time(s) when the velocity is zero. (d) Use your results of part (c) to sketch one period of the position y(t). Clearly indicate the location and magnitude of the maximum value of y(t).