### Lunar Leaper

Gravity on the Moon is about 1/6th that on the Earth. A pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth. How high a pole could he clear on the Moon?

### Stonehenge

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

### Differential Equation Matcher

Match the descriptions of physical processes to these differential equations.

# Pdf Matcher

##### Age 16 to 18 Challenge Level:

I have a series of six probability density functions $X$, each of which satisfies at least one of the following conditions:

1. $X$ is non-negative.
2. $X$ can take any positive value.
3. $X$ is a reasonably realistic pdf for a model of a share price of a bank in a year's time.
4. The probability of $X$ taking a value in the range $(a, b)$ is the same as the chance of $X$ taking a value in the range $(-b, -a)$.
5. $X$ is a reasonably realistic pdf for a model of human life expectancy.
6. There is a number $a$ such that $P(x> a) \geq 2 P(x> 2a)$.

Which of the following six curves (ignoring scale) would be the potential candidates for these mathematical descriptions? Are multiple matches possible? What axes and scales would you choose in each case?