A toboggan with two people on it weighs 300 lb. It starts fromrest down a slope, 1/4 mile long, from a height 200 ft abovehorizontal level. The coefficient of sliding friction is 3/100 andthe force of the wind resistance is proportional to the square ofthe velocity. When the velocity is 30 ft/sec, this force is 6lb.
(a) Find the velocity of the toboggan as a function of thedistance and of the time.
(b) With what velocity will the toboggan reach the bottom of theslide?
(c) When will it reach the bottom?
(d) What would its terminal velocity be if the slide wereinfinite in length?
Answers:
(a) v= 74.1 (e^(0,105t)-1)/(e^(0.105t)+1),v^2=5484(1-e^(-0.0014s)
(b) 68 ft/sec
(c) 30 sec, approx.
(d) 74.1 ft/sec
I'm having trouble solving for v originally. Any help would bemuch appreciated.
