The ball would travel 3 times as high.

The equation for finding the displacement (vertical height in this case) of an object with a constant is:

##v^2 = u^2 -2as##

where ##s## is the displacement

##u## is the initial velocity

##v## is the final velocity

and ##a## is the acceleration .For more information about the resoning behind this formula look here.

We can rearrange this formula to give:

##s = (v^2-u^2)/(2a)##

since we want to know about displacement (height).

When throwing a ball vertically the velocity at the top of the throw (when the ball is highest) is 0 so we can remove the ##v^2## part of the equation as ##0^2 = 0##.

Now we can look at this equation in terms of Earth.

##s_(earth) = (-u^2)/(2a)##

The initial velocity ##u## remains constant in both cases but the acceleration due to gravity on mars is one third the acceleration due to gravity on earth or ##1/3a## so our equation for Mars is:

##s_(mars) = (-u^2)/(2xx 1/3 a)##

This can be rearranged to produce:

##s_(mars) = 3(-u^2)/(2a)##

From this we see that ##s_(mars) = 3(s_(earth))##.

Therefore the displacement or height (##s##) on mars is three times that on earth so the ball will travel 3 times as high .