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I solved part A but not part B:
A batted baseball leaves the bat at an angle of 35.0 degrees above the horizontal and is caught by an outfielder 370 ft. from home plate at the same height from which it left the bat.
Part A: What was the initial speed of the ball?
Answer: 34.3 m/s
Part B: How high does the ball rise above the point where it struck the bat?
Answer: I got 39.6 m but it was incorrect. :(

Physics 
bobpursley,
at the top of the arc, the vertical velocity is zero.
Vtop=Vivertical9.8t
solve then for time to the top.
height=Vivertical*t4.9t62