Solve the all parts of given problem:
Problem: A batted baseball leaves the bat at an angle of 34.0 above the horizontal and is caught by an outfielder 360ft from home plate at the same height from which it left the bat.
Part A: What was the initial speed of the ball?
Part B: How high does the ball rise above the point where it struck the bat?
Please provide a full detailed explanation for the solution.