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## Homework Statement

A rocket is launched vertically and is tracked by a radar station located on the ground 5 mi from the launch pad. Suppose that the elevation angle θ of the line of sight to the rocket is increasing at 3° per second when θ=60°. What is the velocity of the rocket at this instant?

## Homework Equations

c

^{2}=x

^{2}+y

^{2}

tanθ=y/x

## The Attempt at a Solution

5

^{2}=c

^{2}-y

^{2}

25=c

^{2}-y

^{2}

0=2c(dc/dt)-2y(dy/dt)

0=c(dc/dt) - y(dy/dt)

dc/dt=3°=π/60

θ=60°=π/3

tan π/3=y/5

5tan π/3=y

y=3

c

^{2}=5

^{2}+3

^{2}

c

^{2}=square root of 34

Can I just plug in 3 for y, square root of 34 for c, and π/60 for dc/dt