Grey's Jet-ski Adventure

Calculating Grey's Distance and Displacement

Grey decided to take his jet-ski out for a spin and first skied six meters south. This initial movement can be represented as the vertical leg of a right-angled triangle. When Grey turns west and skis eight meters, this can be represented as the horizontal leg of the triangle.

Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can calculate Grey's distance from the dock:

Distance = √(6² + 8²) = √(36 + 64) = √100 = 10 meters.

Grey's displacement from the dock is the shortest distance between his initial and final position. Since he moved south and then west, his displacement forms the hypotenuse of the right-angled triangle. Therefore, his displacement is also 10 meters, the same as his distance from the dock.

It is important to note that distance is a scalar quantity, meaning it only has magnitude, while displacement is a vector quantity that includes both magnitude and direction. In this scenario, Grey's displacement and distance are the same because he ended up in a straight line from the dock.