SOLUTION: A missile is launched and travels along a path that can be represented by: y= the Square root of X A radar tracking station is located 2 km directly behind the launch pad

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Question 328496: A missile is launched and travels along a path that can be represented by:
y= the Square root of X
A radar tracking station is located 2 km directly behind the launch pad. Placing the launch pad at the origin and the radar station at (-2, 0), find the largest angle of elevation required of the radar to track the missile
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
The max angle will be attained by the tangent line to the curve y=sqrt(x) that passes through x=-2. The thing is, we have to find this point on the curve.
We can do this by using the equation of a line formula.
y-y1=m%28x-x1%29
y1=0, x1=-2, y=sqrt(x), m=1/(2*sqrt(x))
sqrt%28x%29-0=1%2F%282%2Asqrt%28x%29%29%2A%28x%2B2%29
Solving for x, we find x=2.
The line is tangent to the curve at (2,sqrt(2)).
By the law of tangents, we can easily find the angle now.
arctan%28sqrt%282%29%2F4%29=19.4712206345 degrees is the max angle.