The boy’s speed is given as 5 ft/sec, but the question is ambiguous as to whether his position remains due north of the starting point, or due north of the girl. Your approach assumes the former, but his 5ft/sec speed may include the girl’s 1ft/sec eastward component.
Technically, his starting location is defined contradictorily, being both the same position as hers, as well as “due north”. We can only proceed if a point can be considered “due north” of itself.
Technically, his initial direction of travel isn’t actually defined, nor is that direction specified as constant. Only his initial position and “5ft/sec” speed has actually been defined. The problem doesn’t actually constrain him to a northerly heading, or even to a constant heading. He could choose to orbit her at a constant distance as she travels eastward.
His possible position will be up to 25ft from the origin, putting him at most 30 feet from her, if his direction is opposite hers. If his direction is constant, his minimum distance from her will be 20 feet.
If his direction is not constant, and he elects to minimize his distance from her, as his distance from her approaches zero, his revolutions around her in a given time will approach infinite, and we will have to consider relativistic effects. From his perspective, his body will be ripped apart into a dizzying pink mist, which he will experience for all eternity. Poetic, I suppose.
The boy’s speed is given as 5 ft/sec, but the question is ambiguous as to whether his position remains due north of the starting point, or due north of the girl. Your approach assumes the former, but his 5ft/sec speed may include the girl’s 1ft/sec eastward component.
The implication that the boy is strafing while maintaining a straight vertical line to the girl is hilarious
Technically, his starting location is defined contradictorily, being both the same position as hers, as well as “due north”. We can only proceed if a point can be considered “due north” of itself.
Technically, his initial direction of travel isn’t actually defined, nor is that direction specified as constant. Only his initial position and “5ft/sec” speed has actually been defined. The problem doesn’t actually constrain him to a northerly heading, or even to a constant heading. He could choose to orbit her at a constant distance as she travels eastward.
His possible position will be up to 25ft from the origin, putting him at most 30 feet from her, if his direction is opposite hers. If his direction is constant, his minimum distance from her will be 20 feet.
If his direction is not constant, and he elects to minimize his distance from her, as his distance from her approaches zero, his revolutions around her in a given time will approach infinite, and we will have to consider relativistic effects. From his perspective, his body will be ripped apart into a dizzying pink mist, which he will experience for all eternity. Poetic, I suppose.