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Hello and thank you in advance for your help

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:
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5.2 m/s
Here is my working out:

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)
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JumpingFun
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I had several math problems I couldn't figure out at all when I was taking Calculus. I searched the web and found these guys - http://goo.gl/RHXaS5 . They really helped me and explained the whole problem to me when I was still confused. Perhaps they can help you too.
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