Final answer:
A baseball would go higher if thrown on the Moon than on Mars due to the Moon's significantly weaker gravitational acceleration. The lesser gravity results in a slower fall, allowing an object thrown with the same velocity to climb higher before descending.
Step-by-step explanation:
A baseball would go higher if thrown from the surface of the Moon than if thrown with the same velocity from the surface of Mars due to the difference in gravitational acceleration on each body. The Moon's gravitational acceleration is approximately 1.62 m/s2, while that of Mars is about 3.71 m/s2. Since the acceleration due to gravity on the Moon is about 1/6th of that on Earth and much less than that on Mars, an object thrown with the same initial velocity will reach a greater height on the Moon due to the lesser force pulling it down.
Considering the physics behind a ball's trajectory, we know that throw height is inversely proportional to the gravitational pull. So, for the same initial velocity, a ball thrown on the Moon would go higher because it would fall slower compared to one thrown on Mars, where the gravity is stronger, bringing it down sooner. Using the knowledge that a safe fall on the Moon can be up to six times higher than on Earth due to lesser gravity, and by analogy, when comparing the Moon and Mars, the difference in gravity would allow for a proportionately higher throw on the Moon.