A bus is going along a straight line with velocity V_b. You are located at a distance D from the bus and distance S away from the road. You can run with a maximum speed V_p in any direction. a. In which directions (the angles from the line connecting you and the bus) can you run in order to catch the bus (reach any point along the road at the same time with the bus)? b. For which minimal speed V_p is this even possible? In which direction should you run in this case? c. Find all the possible locations of the person (on either side of the road) for which they can catch the bus with given V_b and V_p.

A bus is going along a straight line with velocity V_b. You are located at a distance D from the bus and distance S away from the road. You can run with a maximum speed V_p in any direction. a. In which directions (the angles from the line connecting you and the bus) can you run in order to catch the bus (reach any point along the road at the same time with the bus)? b. For which minimal speed V_p is this even possible? In which direction should you run in this case? c. Find all the possible locations of the person (on either side of the road) for which they can catch the bus with given V_b and V_p.