Physics Problem cat chasing mouse-2 dimensional dynamics?

Question

A cat is chasing a mouse. The mouse runs in a straight line at a speed of 1.5 m/s
.If the cat leaps off the floor at a 30 degree angle and a speed of 4.0 m/s, at what distance behind the mouse should the cat leap in order to land on the poor mouse?

Answer 1

The cat's vertical velocity Vy = 4*sin(30). He will be airborne for t=2Vy/g. He gains on the mouse at Vxrel = 4*cos(30)-1.5 m/s, and thus gains Vxrel*t m in the jump, which is the distance his launch point should be behind the mouse.