The vertical velocity of the ball is: [tex](150\frac{ft}{s})(sin52) = 118.2\frac{ft}{s}[/tex]. Since gravity acts at [tex]-32\frac{ft}{s^2}[/tex], this means that the time of flight up to the maximum height (at which vertical velocity is 0) would be:
[tex](0 - 118.2)=(-32)t \\ t = 3.69 s[/tex]
This maximum height is:
[tex]4.8 + 118.2t + 0.5(-32)t^2 \\ = 4.8 + 118.2(3.69) - 16(3.69)^2 \\ = 223.1 ft[/tex]
Then the time for it to fall down will be:
[tex]0.5(-32)(t_{2})^2=-223.1 \\ t_2 = 3.73s[/tex]
The total time will be 3.69 + 3.73 = 7.42 seconds.
