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High Jumping

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Out in Space

A space craft is ten thousand kilometres from the centre of the Earth moving away at 10 km per second. At what distance will it have half that speed?

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Dangerous Driver?

Was it possible that this dangerous driving penalty was issued in error?

Earth Orbit

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

For the first part you will need to change variables in an equation. You will need to use this idea:$$\frac{df}{dr} = \frac{df}{du}\frac{du}{dr}\;.$$ For the second part, you need to redefine your angle by shifting it by a certain amount.