
Arturo O. answered 09/26/17
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There is more than one way to solve this. Here is one way:
You should know from kinematics that the vertical velocity obeys
v(t) = v0 + at = v0 - gt
vo = (35 m/s) sin30° = 17.5 m/s
v(t) = 17.5 - 9.8t, v in m/s, t in seconds
At maximum height, the instantaneous speed is zero.
17.5 - 9.8t = 0
t = 17.5/9.8 s ≅ 1.786 s
Now plug this value of t into the equation of motion:
h(t) = -(1/2)gt2 + v0t = -4.9t2 + 17.5t
and get hmax in meters. You should be able to finish from here.