A small rocket is fired in a test range. It rises high into the air and soon runs out of fuel. On the way down it passes near an observer (sitting in a 21.5-m-high tower) who sees the rocket traveling at a speed of 35 m/s and moving in a vertical plane at an angle of 56° below horizontal.

1. What is the maximum altitude reached?
Vertical speed is= -29.016
Find how far it fall to reach-> -29.016

v=-gt
-29.016=-9.81t
t= 2.961s

Find distance it fell in that time:
d=1/2gt^2
d=4.9(2.961)^2
d=42.961

From its peak height to the height of the observer if fell 42.961m then add the height of the tower (21.5m) this will give max altitude. 64.461m

B. with what speed does the rocket hit the ground?

64.461=1/2gt^2
t= 13.155

from here I am stuck. Any help please.