bballgirlweez said:
The record speed for grass skiing was set in 1985 by Klaus Spinka, of Austria. Suppose it took Spink 6.6s to reach his top speed after he started from rest down a slope with a 34.0 degree incline. If teh coefficint of kinetic frction between the skis and the grass was .198, what was the magnitude of Spinka's net acceleration? what was his speed after 6.60s?
This is a terminal velocity problem, and in an ideal situation, the velocity approaches, but never reaches v_{max} The problem needs to be restated so that Spink took 6.6s to reach a certain percentage of his top speed (like 99.5%, 99%, 98%), and these small changes make a big difference.
Here's a link to terminal velocity formula and it's derviation:
http://www.karlscalculus.org/l12.1.html
I changed the signs for Vmax and acceleration so the formula becomes:
V(t) = V_{max} (1 - e^{-2at/V_{max}})/(1+e^{-2at/V_{max}})
where a is the rate of non-aerodynamic acceleration (negative), t is time, V is velocity (0 or negative) and Vmax is max velocity.
In this case, a is the compenent of gravity - component of friction:
a = (sin(34)\ g) - (cos(34)\ g\ .198) = -9.8m/s^2\ (.559 - .164) = -3.87m/s^2
However, stuck, at t = 0, you end up with
V(0) = V_{max}*(0)/(2) = 0
and at t = \infty you end up with
V(\infty) = V_{max}*(1)/(1) = V_{max}
So as I orignally stated, you can't reach maximum velocity in any finite amount of time in this idealized case. However, if you knew that a certain percentage of Vmax was reached in 6.6 seconds, you could then solve for Vmax. As this percentage approaches 100%, Vmax approaches 0, aerodynamic drag approaches infinity, and vice versa.
