M2 question, help neededWatch
The question comes from the AQA mechanics two book by Brian Jefferson.
It is question 14 of exercise 4D:
A cyclist and her cycle have a combined mass of 80 kg. The resistance to motion is proportional to the speed. On the level, she can travel at a maximum speed of 10 m/s, and she can freewheel down an incline of angle theta at 14 m/s. Find the maximum speed at which she can go up the same incline.
This seemed like an easy question but I failed to get the answer at the back of the book.
answer at the back of the book:
P = F*V , resistant force = kv
P = 100k
P = (80 g sin @ - 14k) *14 *** @ = theta
P = (Vk + 80 g sin @) *V
some small manipulation later to find V
0 = V^2 + V(148/7) - 100
This gives V = 3.98 m/s
since V must be smaller than 10 and larger than 0, I chose up the hill to be my positive (other result is around -25)