To find the relative velocity of vehicle P with respect to vehicle Q, follow these steps:
1. Identify the velocities:
- Velocity of P ([tex]\( v_P \)[/tex]) = 5 m/s towards the west.
- Velocity of Q ([tex]\( v_Q \)[/tex]) = 15 m/s towards the west.
2. Understand the context:
- Since both vehicles are moving in the same direction (towards the west), the relative velocity of one vehicle with respect to the other is found by taking the difference between their speeds.
3. Applying the relative velocity formula:
- The relative velocity of P with respect to Q ([tex]\( v_{PQ} \)[/tex]) is given by the formula:
[tex]\[
v_{PQ} = v_Q - v_P
\][/tex]
4. Substitute in the values:
- [tex]\( v_Q = 15 \)[/tex] m/s
- [tex]\( v_P = 5 \)[/tex] m/s
Plugging these values into the formula, we get:
[tex]\[
v_{PQ} = 15 \, \text{m/s} - 5 \, \text{m/s} = 10 \, \text{m/s}
\][/tex]
5. Result interpretation:
- The relative velocity of P with respect to Q is 10 m/s.
So, the relative velocity of vehicle P with respect to vehicle Q is [tex]\( 10 \, \text{m/s} \)[/tex].
