Question

two students are riding bicycles. the diagram shows their relative rates of motion.
what is the westward rate of motion of student 1 relative to the ground?
8 km/hr
12 km/hr
20 km/hr
32 km/hr

Explanation:

Step1: Define the velocities

Let the velocity of student 1 relative to the ground be \(v_{1,g}\), the velocity of student 2 relative to the ground be \(v_{2,g} = 12\space km/hr\) (east, so we can consider east as positive and west as negative), and the velocity of student 1 relative to student 2 be \(v_{1,2}=- 20\space km/hr\) (west).
The formula for relative velocity is \(v_{1,2}=v_{1,g}-v_{2,g}\).

Step2: Solve for \(v_{1,g}\)

Rearrange the formula \(v_{1,g}=v_{1,2}+v_{2,g}\).
Substitute the values: \(v_{1,g}=-20 + 12\).
\(v_{1,g}=-8\space km/hr\). The negative sign indicates the west - ward direction.

Answer:

8 km/hr