Calculating the coordinates and direction of displacement and position vectors

Learning Goals:
• Understanding the connection between initial, final, and displacement vectors.
• Practicing right triangle geometry, the Pythagorean theorem, and arctangent calculation.

Problem statement:
Gerry, the gerbil, walks 55 cm in the positive y-direction. After this, he is located 95 cm from the origin at an angle of 50° from the positive x-axis towards the positive y-axis, as shown in the figure.
a) Complete the figure by including the change in position and the initial position vectors.
b) Calculate Gerry’s initial position.

00:19 – Reading the problem statement and analyzing it
00:54 – Part (A) Sketching the initial and displacement vectors.
02:20 – Part (B) Method 1: Finding the coordinates of the initial position vector.
02:58 – Part (B) Method 2: Finding the length and direction of the initial position vector.