In the figure here, a small, solid, uniform ball is to be shot from point P so that it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distance d from the right edge of the plateau. The vertical heights are h, = 3.5 cm and h, = 1.70 cm. With what speed must the ball be shot at point P for it to land at d = 4.5 cm? Ball

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In the figure here, a small, solid, uniform ball is to be shot from point \( P \) so that it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distance \( d \) from the right edge of the plateau. The vertical heights are \( h_1 = 3.5 \, \text{cm} \) and \( h_2 = 1.70 \, \text{cm} \). With what speed must the ball be shot at point \( P \) for it to land at \( d = 4.5 \, \text{cm}? \)

**Diagram Explanation:**

- **Ball Path:** The diagram shows a ball at point \( P \) on a flat surface, represented by a horizontal line. An arrow next to the ball indicates the direction of the ball's movement.
  
- **Ramp:** The path then curves upward to form a ramp leading to a higher level, on a plateau. 

- **Plateau:** The plateau is a flat horizontal section following the ramp.

- **Vertical Heights:** Two vertical measurements are indicated:
  - \( h_1 = 3.5 \, \text{cm} \) is the height of the plateau from the base level.
  - \( h_2 = 1.70 \, \text{cm} \) is the height drop from the plateau edge down to the landing point.
  
- **Horizontal Distance \( d \):** A horizontal line labeled \( d \) marks the distance from the edge of the plateau to the landing point where the ball is supposed to land. This distance is given as \( d = 4.5 \, \text{cm} \).
Transcribed Image Text:In the figure here, a small, solid, uniform ball is to be shot from point \( P \) so that it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distance \( d \) from the right edge of the plateau. The vertical heights are \( h_1 = 3.5 \, \text{cm} \) and \( h_2 = 1.70 \, \text{cm} \). With what speed must the ball be shot at point \( P \) for it to land at \( d = 4.5 \, \text{cm}? \) **Diagram Explanation:** - **Ball Path:** The diagram shows a ball at point \( P \) on a flat surface, represented by a horizontal line. An arrow next to the ball indicates the direction of the ball's movement. - **Ramp:** The path then curves upward to form a ramp leading to a higher level, on a plateau. - **Plateau:** The plateau is a flat horizontal section following the ramp. - **Vertical Heights:** Two vertical measurements are indicated: - \( h_1 = 3.5 \, \text{cm} \) is the height of the plateau from the base level. - \( h_2 = 1.70 \, \text{cm} \) is the height drop from the plateau edge down to the landing point. - **Horizontal Distance \( d \):** A horizontal line labeled \( d \) marks the distance from the edge of the plateau to the landing point where the ball is supposed to land. This distance is given as \( d = 4.5 \, \text{cm} \).
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