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# Complicated maths question? Need help?

How do you do this question?

1. A space shuttle was launched straight up, and its altitude is given by h = 10 t^2 after t seconds. You are on the ground 500 metres away from the launch site watching the shuttle going up. The line of sight from you to the rocket makes an angle x with the horizontal. By how many radians per second is x changing ten seconds after the launch?

### 1 Answer

Relevance

- Anonymous8 years agoFavorite Answer
h = 10t²

Differentiate.

dh/dt = 20t

h = 500tan(x)

Differentiate.

dh/dx = 500sec²(x)

dx/dt = dx/dh dh/dt

dx/dt = dh/dt ÷ dh/dx

dx/dt = 20t ÷ 500sec²(x)

dx/dt = 20t ÷ 500(1 +tan²x)

dx/dt = t ÷ 25(1 + tan²x)

At t = 10, h = 1000 and 1000=500tanx so tanx = 2

dx/dt = 10 ÷ 25( 1 + 2²) = 10 ÷ 125 = 0.08 rad/s

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