Certainly! Let's solve the problem step-by-step:
1. First, identify the velocities given in the problem:
- The velocity of the truck moving west is [tex]\(12 \, \text{m/s}\)[/tex].
- The velocity of the person running on the truck from point [tex]\(A\)[/tex] to point [tex]\(O\)[/tex] is [tex]\(3 \, \text{m/s}\)[/tex].
2. Understand the directions of movement:
- The truck is moving west at [tex]\(12 \, \text{m/s}\)[/tex].
- The person is running on the truck in the same direction (west) at [tex]\(3 \, \text{m/s}\)[/tex] with respect to the truck.
3. To find the velocity of the person with respect to the road, add the velocity of the truck and the velocity of the person on the truck. Since both velocities are in the same direction (west), we can directly sum them:
[tex]\[
\text{Velocity of the person with respect to the road} = \text{Velocity of the truck} + \text{Velocity of the person on the truck}
\][/tex]
4. Substitute the given velocities into the equation:
[tex]\[
\text{Velocity of the person with respect to the road} = 12 \, \text{m/s} + 3 \, \text{m/s}
\][/tex]
5. Perform the addition:
[tex]\[
\text{Velocity of the person with respect to the road} = 15 \, \text{m/s}
\][/tex]
Therefore, the velocity of the person with respect to the road is [tex]\(15 \, \text{m/s}\)[/tex], moving west.
