Optimizing Thrown Ball Trajectories

[Bryon]

Homework Statement

An astronaut in his space suit can throw a ball a maximum distance dmax = 9 m on the surface of the earth.

For a given speed of the ball, what angle to the horizontal q (in degrees) will yield the greatest range? 45 degrees

If the ball is thrown at this same angle q, what speed will produce this greatest range (9 m) ? 9.3m/s

How far can he throw the ball on a planet where g1 = 22 m/s2? 4.009

What height will the ball reach on this "maximum range" trajectory? (on the planet where g1 = 22 m/s2)? I am having a problem with this one. I need help!

Homework Equations

v(y) = v(initial)*sin(angle)
v(y) = v( y initial) + at
y = y(initial) + 0.5(v(inital) + v)t

The Attempt at a Solution

v(y) = 9sin(45) = 6.57

0 = 6.57 + 22(t)
t = 0.298

y = 0 + 0.5(6.57 + 0)*(0.298)
y = 0.978

Where did I go wrong? Did I need the vertial acceleration?

thanks!

 

[rl.bhat]

(y) = 9sin(45) = 6.57
It should be
(y) = 9.3sin(45)

 

[Bryon]

Ah yes I made a type, it should be 9.3. But I still am having trouble finding the maximum height...It seems that every approach I've tried it comes up wrong.

 

[rl.bhat]

Ah yes I made a type, it should be 9.3. But I still am having trouble finding the maximum height...It seems that every approach I've tried it comes up wrong.

t = 0.2986
= 0.299