The vertical displacement is given by:
h = v(sin theta)t + 1/2 (-9.8) t^2
And h' is the vertical velocity at any time.......this is 0 at the max ht.
And h' = vsin(theta) - 9/8t = 37sin(44.9) - 9.8t ...... set to 0
37*sin(44.9) = 9.8t
37*sin(44.9)/ 9.8 = t = 2.665 s
And putting this back into the position function, the max ht. =
h(2.665) = about 34.8 m
Here's the graph : https://www.desmos.com/calculator/smv5klqan8
