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The problem shown in the image involves a comparison between the speed of a ball just before hitting the ground when projected horizontally on both the Earth and the Moon. The key concepts are horizontal projectile motion and the influence of gravitational acceleration.

### Problem Breakdown:

- A ball is projected horizontally with an initial speed \( v_0 \) from a height \( h \) on Earth. Its speed before touching the ground is \( v_e \).
- The experiment is repeated on the Moon, where the ball is also projected horizontally from the same height and with the same initial speed \( v_0 \), but the gravitational acceleration on the Moon is lower.
- The question asks which speed is greater, \( v_e \) or \( v_m \) (where \( v_m \) is the speed on the Moon), and why.

### Key Factors:
1. **Vertical motion** is influenced by gravitational acceleration:
   - Earth's gravitational acceleration is \( g_e \), and the Moon's is \( g_m \) (where \( g_m < g_e \)).
   - The ball’s vertical velocity increases due to gravity over time, but the time to hit the ground is greater on the Moon because the gravitational force is weaker.
   
2. **Horizontal motion** remains unchanged because there is no horizontal force acting on the ball:
   - The horizontal velocity \( v_0 \) remains constant on both the Earth and the Moon since gravity only affects vertical motion.

3. **Total speed** before impact is a combination of the horizontal and vertical components of velocity:
   \[
   v_{\text{total}} = \sqrt{v_0^2 + v_{\text{vertical}}^2}
   \]
   The vertical component \( v_{\text{vertical}} \) will be smaller on the Moon because the ball accelerates slower in the vertical direction due to weaker gravity.

### Analysis of Answer Choices:
- **Choice A:** Incorrect. While the ball on the Moon will travel a greater horizontal distance due to weaker gravity, this does not directly answer which speed is greater.
- **Choice B:** Correct. The ball on the Moon experiences less acceleration, meaning it has a smaller vertical velocity component compared to the ball on Earth when it hits the ground. Thus, \( v_m \) is greater than \( v_e \).
- **Choice C:** Incorrect. This choice incorrectly claims that \( v_e \) is greater due to a smaller vertical component on the Moon, but the opposite is true.
- **Choice D:** Incorrect. This choice confuses horizontal distance with total speed, which includes both horizontal and vertical components.

### Final Answer: **B.** The ball on the Moon has less vertical acceleration, leading to a smaller vertical velocity, so its total speed just before hitting the ground, \( v_m \), is greater than that on Earth, \( v_e \).

Would you like further explanation, or have any questions?

Here are 5 related questions:
1. How do horizontal and vertical motions in projectile motion differ?
2. What effect does gravity have on the vertical velocity of a projectile?
3. How is total velocity calculated for a projectile in two dimensions?
4. Why is the horizontal velocity of a projectile constant in the absence of air resistance?
5. What are the key differences between projectile motion on Earth and the Moon?

**Tip:** In projectile motion, always separate the horizontal and vertical components when analyzing velocity and acceleration.

A ball is projected horizontally with initial speed v0 from a platform of height h on Earth. The ball's speed immediately before touching the ground is ve. The experiment is repeated on the Moon so that the ball is projected horizontally with the same speed from the same height. The acceleration due to gravity is less on the Moon than on the Earth. The ball’s speed just before touching the ground is vm. Which speed is greater, and why?

Compare the speed of a ball projected horizontally on Earth and the Moon just before it hits the ground. Learn how gravitational acceleration affects vertical velocity and total speed in projectile motion.

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