9) \( \overline{\mathrm{AB}} \) is a straight road of length 5 km . a man moved from A towards B with uniform speed 6 km . /hr. and at the same moment another man moved from B towards A with uniform speed 4 km ./hr., then the two men will meet each other .............. (a) after one hour from beginning of motion. (b) at the middle of the road. (c) after half hour from beginning of motion. (d) at a distance of 3 km . from B

To solve this problem, we first need to determine how long it will take for both men to meet each other. The combined speed of both men is the sum of their individual speeds: \[ 6 \text{ km/hr} + 4 \text{ km/hr} = 10 \text{ km/hr}. \] Since they are moving towards each other, we can find the time it takes for them to meet by using the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}}. \] The distance they are covering together is 5 km, so: \[ \text{Time} = \frac{5 \text{ km}}{10 \text{ km/hr}} = 0.5 \text{ hr} \text{ or } 30 \text{ minutes}. \] So, the two men will meet each other after half an hour from the beginning of their motion. Therefore, the correct answer is: (c) after half hour from beginning of motion. The additional relevant knowledge: One fascinating aspect about meetings on a straight road is that it's often used in physics problems to illustrate relative motion. This concept helps learners grasp how different speeds can affect the timing and distance between two moving objects. It’s a simple yet effective way to show that teamwork—albeit involuntary here—can lead to a timely rendezvous! In real-life situations, this scenario could resemble two friends walking towards each other in a park. If they keep track of their speeds, they can efficiently time when to meet at the perfect spot, allowing for a fun catch-up without lengthy waits!