Solve the all parts of given question:
Question: A person jumps from a platform to the ground. The platform is 3 m high and the person's initial takeoff velocity is 10m/s at an angle of 45 degrees with respect to the horizontal. The distance between takeoff point and the edge of the platform is 1 m.
Part I: Find the horizontal displacement between the takeoff point and the landing point.
Part II: How long does it take when the person's feet touch the ground?
Part III: What is the landing velocity (both magnitude and direction/angle with respect to horizontal)?
Show your reasoning and calculations for above question.