Final answer:
The ball's maximum height on Mars would be greater compared to Earth when thrown with the same velocity, because Mars has approximately one third of Earth's gravitational acceleration.
Step-by-step explanation:
If you throw a ball upward with the same velocity on Mars as on Earth, the ball's maximum height on Mars would be greater than on Earth. This is because the free fall acceleration on Mars is about one third that on Earth. To understand this, we use the formula h = v^2 / (2 * g), where h is the maximum height, v is the initial velocity, and g is the acceleration due to gravity. Since the initial velocity v remains the same and the acceleration due to gravity g on Mars is one third that of Earth's, the height h on Mars would be three times that on Earth.
Let's assume the ball is thrown upward with the same initial velocity on both Mars and Earth. On Mars, due to the weaker gravitational acceleration, the ball will decelerate more slowly while moving upward, and this deceleration will continue until the ball reaches its maximum height and starts moving downwards. On Earth, the stronger gravitational acceleration will cause the ball to decelerate more quickly, resulting in a higher maximum height compared to Mars.
Therefore, the ball's maximum height on Mars will be lower than that on Earth.