Vector problem please help.?

Question

I'm really dumb for not getting this one but I'm really exhausted after 60 problems. So a guy tosses a basket ball into a hoop that is 3.048 m high at an angle of 47 degrees and a velocity of 17 m/s. The man's height is 2.554 m. How long does it take the ball to achieve its maximum height (the half g a^2 formula is not working for me). How long for it to reach the hoop and the horizontal length of the shot. I've been up all night so please help me.

Answer 1

Vy = 17sin47°
Vx = 17cos47°
1. time to max height
t1 = Vy/g = (17/9.80665)sin47°
t1 ≈ 1.2678144858362333942669761172965
max height:
h = 2.554 + (17sin47°)^2 / (2*9.80665)
h ≈ 10.435376946053244786044472459278
time to drop to hoop:
t2 = √2(10.43538 - 3.048)
t2 ≈ 3.843794
2. total air time
t3 = t1 + t2
t3 ≈ 5.111609
3. horizontal length of shot:
d = Vxt3 = (17cos47°)(5.111609)
d ≈ 59.26385