Calculate Direction to Intercept Object in Vector Mechanics

[research1]

Mechanics question. I've had 4 different answers from 4 different people and am still none the wiser to this teaser.


A river flows North to south. A rower on the lefthand bank (call this 0 , 0) facing north spots an object. The object is at 50sin20 (co ords 17.1 , 47). The current is running south at 3m/s. The rower can maintain a rowing speed of 4m/s. The current will affect both rower and object.

Calculate the direction with respect to the riverbank the rower must row in order to intecept the object.

 

[DeShark]

I think this question is best answered by changing reference frames...

Let's say the rower has just begun his row... he's not taken a single stroke, but he's in the water. This is our t=0. At this point, according to the rower, the object is at 50sin(20). If things continues like this, both rower and object will travel at the same speed downstream, never getting further apart nor closer together, the object will remain at 50sin(20), *according to the rower*. So he must always row at a 20 degree angle to north. He does this at 4 metres/second... and gets there in (50m)/(4m/s) = 12.5 seconds... as far as I can tell. This seems like one of those problems which seems a lot harder to do. It's a conceptual thing.

 

[research1]

I thought that originally but then a few people got really mathematical about it.

Say now that the rower got it wrong and the object was 70 metres away at 25 degrees. The rower remains on the original course (i.e sin20). Now he won't intercept the object but what is the closest that he will get?