Final answer:
To find when two vehicles traveling in perpendicular directions will be closest to each other, one must use the principles of relative motion and kinematics, involving the relative velocities and directions of the vehicles.
Step-by-step explanation:
The question involves determining the point at which two vehicles traveling in perpendicular directions will be closest to each other and how far apart they will be at that moment. This is a classic physics problem that can be solved using the principles of relative motion and kinematics.
To solve for the time when the vehicles will be closest, we have to consider the relative speeds and directions of the truck and the car. The truck is moving east at 80 km/h, and the car is moving north at 50 km/h. Since these velocities are perpendicular, we can use the Pythagorean theorem to find the relative velocity between the two vehicles. Then, we would apply kinematic equations to determine when the distance between them is at a minimum.
Similarly, to find the distance between the vehicles at the closest point, we require both the relative velocity and the time at which this minimum distance occurs, which can calculated from the kinematic equations that relate velocity, distance, and time.
Note: The specific calculations and solutions are not provided here, as the actual values for the time and distance at which the vehicles will be closest are not given in the example text provided.