# Mathematical Modelling - Upper Secondary

### Where to Land

##### Stage: 4 Challenge Level:

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?

### Slippage

##### Stage: 4 Challenge Level:

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance up the wall which the ladder can reach?

### Big and Small Numbers in Physics - Group Task

##### Stage: 5 Challenge Level:

Work in groups to try to create the best approximations to these physical quantities.

### Dangerous Driver?

##### Stage: 5 Challenge Level:

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

### Model Solutions

##### Stage: 5 Challenge Level:

How do these modelling assumption affect the solutions?

### 10 Olympic Starters

##### Stage: 5 Challenge Level:

10 intriguing starters related to the mechanics of sport.

### The Not-so-simple Pendulum 1

##### Stage: 5 Challenge Level:

See how the motion of the simple pendulum is not-so-simple after all.

### Relative Time

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 25 - 2014
Albert Einstein is experimenting with two unusual clocks. At what time do they next agree?

### Trolley Park

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 14 - 2016
In a supermarket, there are two lines of tightly packed trolleys. What is the length of one trolley?

### Mathematical Modelling - Short Problems

##### Stage: 3 and 4

A collection of short Stage 3 and 4 problems on Mathematical Modelling.

### London Eye

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 18 - 2014
The 80 spokes of the giant wheel The London Eye are made from 4 miles of cable. What is the approximate circumference of the wheel?