Relative Velocity Puzzle?

📌 CONCEPT: Relative velocity is the velocity of an object with respect to another object when their velocities are added vectorially.

📐 RULE / FORMULA: The relative velocity of two objects can be calculated using the formula:

💡 WORKED EXAMPLE: A bird is flying at a velocity of 30 m/s in a direction making an angle of 60° with the horizontal. It meets car A, which is moving at 20 m/s due east. To find the relative velocity of the bird with respect to car B, which is moving at 15 m/s due north, we first find the resultant velocity of the bird with respect to car A. Using the formula v = √(v_x^2 + v_y^2), we get v = √(30^2 + 30√3^2) = 45 m/s. The direction of the resultant velocity is 60° with the horizontal. Now, we find the resultant velocity of the bird with respect to car B by adding the velocities vectorially. The resultant velocity is 45 m/s at an angle of 60° with the horizontal.

⚠️ COMMON MISTAKE: Students often forget to add the velocities vectorially to find the resultant velocity, resulting in incorrect answers.