Three balls (1, 2, 3) roll on the surface of a table at different speeds (V₁, V₂, V3). If the balls fall from the table at teh same time and follow the parabolic trajectories shown below, which ball takes longer to land? O O O O b n d All three balls land simultaneously. 2 1 3

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Chapter1: Units, Trigonometry. And Vectors
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**Question:**

Three balls (1, 2, 3) roll on the surface of a table at different speeds (\(v_1, v_2, v_3\)). If the balls fall from the table at the same time and follow the parabolic trajectories shown below, which ball takes longer to land?

**Image Description:**

Three parabolic trajectories are shown originating from a horizontal surface (table) to the ground. Each parabola represents the path of one ball: 

- Ball 1 (with speed \(v_1\)) follows the leftmost trajectory.
- Ball 2 (with speed \(v_2\)) follows the middle trajectory.
- Ball 3 (with speed \(v_3\)) follows the rightmost trajectory.

The parabolas indicate that the initial horizontal speed of each ball is different, but they follow the same vertical drop distance.

**Options:**

- a) All three balls land simultaneously.
- b) 2
- c) 1
- d) 3 (selected)

From the parabolic paths, it is noted that:

- Ball 1 (left trajectory, \(v_1\)) has the shortest horizontal range.
- Ball 2 (middle trajectory, \(v_2\)) has a moderate horizontal range.
- Ball 3 (right trajectory, \(v_3\)) has the longest horizontal range.

Since all balls fall from the same height, the only factor affecting the time to land is their vertical motion, which is independent of their horizontal velocities. Therefore, **all three balls land simultaneously**.

The correct answer is **a) All three balls land simultaneously**.
Transcribed Image Text:**Question:** Three balls (1, 2, 3) roll on the surface of a table at different speeds (\(v_1, v_2, v_3\)). If the balls fall from the table at the same time and follow the parabolic trajectories shown below, which ball takes longer to land? **Image Description:** Three parabolic trajectories are shown originating from a horizontal surface (table) to the ground. Each parabola represents the path of one ball: - Ball 1 (with speed \(v_1\)) follows the leftmost trajectory. - Ball 2 (with speed \(v_2\)) follows the middle trajectory. - Ball 3 (with speed \(v_3\)) follows the rightmost trajectory. The parabolas indicate that the initial horizontal speed of each ball is different, but they follow the same vertical drop distance. **Options:** - a) All three balls land simultaneously. - b) 2 - c) 1 - d) 3 (selected) From the parabolic paths, it is noted that: - Ball 1 (left trajectory, \(v_1\)) has the shortest horizontal range. - Ball 2 (middle trajectory, \(v_2\)) has a moderate horizontal range. - Ball 3 (right trajectory, \(v_3\)) has the longest horizontal range. Since all balls fall from the same height, the only factor affecting the time to land is their vertical motion, which is independent of their horizontal velocities. Therefore, **all three balls land simultaneously**. The correct answer is **a) All three balls land simultaneously**.
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