Day: October 28, 2019

Loopy Lines

You will need to use geometry and algebra to solve this challenge.

Graph of Loopy Lines for this challenge.

We begin this challenge with 2 points. These points are at (1, 1) and (-1, 2). You may know that it only takes 2 points to define a line. You may have guessed that that is what we will use these points for. A second line is drawn, and it passes through the point (3, -2). A third line is then drawn, and it passes through points (2, 3) and (4, 0). A circle is drawn from the 3 intersection points. The radius of the circle is 5 units. The challenge is to find it’s centre.

solution

Unbalanced Balance

Physics is needed for this challenge.

Depiction of scene for Unbalanced Balance.

There is a lever. On one side is a bucket with negligible weight. On the other is a 10 kilogram weight. The bucket is a metre to the left of the pivot, the weight, 2 to the right. Lever has an additional 50 centimetres of unoccupied space. The weight of the lever is 1 kilogram per metre. The weight is attached to a string, and the string goes around a pulley. On the other side is a 7 kilogram weight. The challenge is to figure out how much water at 20° celsius must be poured into the bucket to balance the scale.

solution