You all know that going up a hill slows down your pace, but by how much?
We will try and provide a mathematical model to describe this situation.
Problem 1
What factors will affect you average walking time up a hill?
In this analysis, we will assume that the walking time depends on four factors:
The model will be assumed to be of the form
where T is the time taken.
Problem 2 Use the experimental data given below to find the approximate values for x and y.
Map distance | Height climbed | Walking time |
---|---|---|
d (miles) |
h (feet) |
T (hours) |
12 |
1500 |
5½ |
15 |
2000 |
7 |
Problem 3 Use the model to determine how long it might take to climb up Mount Snowdon, 3560 feet high, if the horizontal distance from your starting point is 3 miles.
Problem 4 If it takes 8 hours to climb a hill and you map distance is 4 miles, estimate the height of the hill.
EXTENSIONS
1. Apply this test to a local situation, using your own experimental data, to see if this model works in practice.
2. Can you produce a model for the time it takes to come down a hill?