Related rates and implicit differentiation

blade123
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Homework Statement


A plane flying with a constant speed of 300 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 30 degrees. At what rate is the distance from the plane to the radar station increasing a minute later?

Homework Equations


a2+b2=c2

The Attempt at a Solution


I got to (y+1)2+x2=d22

It's that extra kilometer that's bothering me. It gives the answer as approx 296 km/h

d1 is the distance between the starting and current point (5 km) and d1' is 300 km/h

I don't know how to get from d1 to d2
 
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Of course, right as I post it I figure it out.

x2+y2=d12

Sub in, differentiate, solve. I'm going to leave it up, just for anyone who wants to check it out. Silly me...
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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