Sounds good! From here, we can determine the path taken by the ball using Mars' gravity, which is approximately `3.72076 m/s²`.
A 45 degree angle forms a right isosceles triangle with the direction of gravity, and means that the horizontal and vertical components of the ball's velocity are equivalent.
To calculate this, we can either apply trigonometry; `30·sin(45) = 30·cos(45) = 15√2`, or Pythagorean theorem; `x² + x² = 30²`, `x² = 450`, `x = 15√2`. Either way, we determine the horizontal and vertical velocities to be `15√2 m/s`.
Because the ball's acceleration due to gravity is `3.72076 m/s²`, we can take the integral of this value with respect to time, to determine the ball's vertical velocity to be `-3.72076t + C`, where t is time measured in seconds, and C is the constant of integration, in this case the known value of `15√2`. Therefore, the equation for the ball's vertical speed is `-3.72076t + 15√2 m/s`.
If we assume effects such as planet curvature and friction are negligible, we can then determine that the ball will reach its highest point when the result of this equation is zero, which occurs at `15√2/3.72076 = 5.70131 s`.
We can then in turn integrate once again to form the equation for the ball's vertical displacement, which would be `-1.86038t² + 15√2t + C`, this time with C being 0, as the ball starts on the ground. Hence, we can simplify the equation to `-1.86038t² + 15√2t`.
In order to calculate the time of impact, we can solve the displacement equation by equating it with 0, giving us the two points in time where the ball is on the ground. `-1.86038t² + 15√2t = 0` can be factorised into `t(15√2-1.86038t) = 0`, giving us the two roots, `t = 0 s` and `t = 11.40262 s`.

We now have all the information we need to determine the highest point reached and the final distance travelled.
Using the time of highest point `t = 5.70131 s`, we can plug that into the vertical displacement equation `-1.86038t² + 15√2t`, which gives us a height of approximately `60.47152 m`.
As was implied that no external forces affect the ball besides gravity, we can assume the horizontal speed of the ball to be constant. Therefore, it will maintain the original speed of `15√2 m/s` we calculated in the beginning, meaning we can simply multiply it by the final time of `11.40262 s` to get the total horizontal distance travelled, which can be estimated at `241.88610 m`.

Please let me know if this explanation was detailed enough for you!
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