# Related rates

## Homework Statement

An RAAF Roulette aeroplane is performing a low fly over at an air show. Under the current wind conditions its top speed is 450 km/hour, and it will fly directly over the crowd at an altitude of only h=340metres approaching from the North. When the aeroplane is only x=180metres horizontally from a person in the crowd looking North, how fast are they rotating their head upwards to keep the aeroplane in the centre of their vision?

You should neglect the height of the person in your calculations. Give your answer in radians per second, either exactly or correct to three decimal places.

## Homework Equations

would I need to use pythagoras to solve this?
Does this mean that dx/dt is 450?

Any help would be much appreciated

haruspex
Homework Helper
Gold Member
would I need to use pythagoras to solve this?
Does this mean that dx/dt is 450?
You will need to use trig and calculus. I would recommend working ent irely algebraically (no numbers!) until the final step, and don't forget to convert to standard units.

You will need to use trig and calculus. I would recommend working ent irely algebraically (no numbers!) until the final step, and don't forget to convert to standard units.

does this mean:

s^2=h^2+x^2

differentiating

2s=2h+2x

s=h+x

what would I so now?

cnh1995
Homework Helper
Gold Member
You are asked to find how fast the angle of vision is changing(w.r.t.ground, since height of the person is neglected). Form an equation which relates this angle to the given quantities. That's where trigonometry comes into picture. Start with a diagram. It will make a lot of things clear for you.

Last edited:
Mark44
Mentor
does this mean:

s^2=h^2+x^2

differentiating

2s=2h+2x
No, this makes no sense. From ##s^2## to 2s, you are apparently differentiating with respect to s, but from ##h^2## to 2h, you're differentiating with respect to h. You are also differentiating ##x^2## with respect to x.

In other words, ##\frac{d s^2}{ds} = 2s## and ##\frac{d h^2}{dh} = 2h##. If you differentiate both sides of an equation, the differentiation must be done with the same variable.

What you're missing is that s, h, and t are all functions of t.
53Mark53 said:
s=h+x

what would I so now?