Brilliant dwellers, can anyone help me with a physics question?
In a 2D plane, a particle moves along the \(x\) axis at the speed of \(1 \, m/s\), with its initial position at \((0, 0)\). Another particle, with initial position \((0, 1)\), starts to chase the first particle with a constant speed of \(2 \, m/s\) in such a way that its trajectory is defined instantaneously by the vector created by the particles (all of the units of the plane are in meters). Ignoring any interactions between the particles, as well as forces such as gravity, answer the following:
1) What kind of curve does the chasing particle define in the plane?
2) At which point do the particles meet?
3) How long does it take until the chasing particle catches up to its target?
I really have no clue as to how to work this out; I tried applying Calculus concepts, but I couldn't come up with a solution. If anyone can help me out here, I'd appreciate it a lot.