Vectors and Beyond (two problems)

[pippintook]

First Problem- Nursery Rhyme Style:

When the three blind mice were running after the farmer's wife, they first ran two meters east, then three meters north, and then four meters southwest, at which point the farmer's wife lay hold to a carving knife. How far are the mouse-tails from their original point of departure?

After drawing it out and trying various equations, I am pretty sure it's close to two meters. But I don't know how to solve it.Second Problem- Astronaut Style

A spacecraft is maneuvering in Cartesian Space at 30 m/s to fetch some space debris as part of Operation Clean Sweep. The debris is floating along the x-axis at a constant speed of 10 m/s. If the debris when first sighted is at coordinates (100, 0), and if the spacecraft is at coordinates (100, 100), in what direction should the spacecraft proceed in order to intercept the debris?

This one...I drew it out, but again, have no idea what to do.

Help please?

 

[Kurdt]

The first question is basically vector addition. Have you been taught that?

For the second part you need to set up some equations of motion. You know that the spacecraft and the debris must get to the same point on the x-axis at the same time if they are to intercept.