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**Question Number:** 22.
**Question Stem:**
如图, 一小球从斜坡 O 点以一定的方向弹出, 球的飞行路线可以用二次函数 y = ax^2 + bx (a < 0)刻画, 斜坡可以用一次函数 y = (1/4)x 刻画, 小球飞行的水平距离 x(米)与小球飞行的高度 y(米)的变化规律如下表:
**(As shown in the figure, a small ball is projected from point O on an inclined plane in a certain direction. The trajectory of the ball can be described by the quadratic function y = ax^2 + bx (a < 0). The inclined plane can be described by the linear function y = (1/4)x. The table below shows the relationship between the horizontal distance x (meters) traveled by the small ball and its height y (meters):)**
**Mathematical Formulas/Equations:**
y = ax^2 + bx (a < 0)
y = (1/4)x
y = -5t^2 + vt
**Table Content:**
| x | 0 | 1 | 2 | m | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| y | 0 | 7/2 | 6 | 米^ | 8 | 巧一/2 | n | 易一/ |
**Sub-questions:**
(1) ① m = n = ______
(1) ② 小球的落点是 A, 求点 A 的坐标.
**(The landing point of the small ball is A. Find the coordinates of point A.)**
(2) 小球飞行高度 y(米)与飞行时间 t(秒)满足关系 y = -5t^2 + vt.
**(The relationship between the height y (meters) and flight time t (seconds) of the small ball satisfies y = -5t^2 + vt.)**
① 小球飞行的最大高度为______米;
**(The maximum height of the small ball flight is ______ meters;)**
② 求 v 的值.
**(Find the value of v.)**
**Chart/Diagram Description:**
* **Type:** Coordinate system with a curved trajectory and a straight line segment.
* **Coordinate Axes:** Horizontal axis labeled x/米 (x/meter). Vertical axis labeled y/米 (y/meter). Origin labeled O.
* **Main Elements:**
* Origin O: Located at the origin (0,0) of the coordinate system. It is the starting point for both the inclined plane and the trajectory. Labeled "O".
* Inclined Plane: A straight line segment starting from O and passing through point A. It is labeled "斜坡". It is described by the equation y = (1/4)x (implied from the text).
* Trajectory: A curved line starting from O and ending at point A. It represents the path of the small ball in flight. It is labeled "小球". The curve is a downward opening parabola segment, consistent with the quadratic function y = ax^2 + bx with a < 0. The peak of the parabola is shown to the left of point A.
* Point A: Located on the inclined plane where the trajectory intersects it (other than O). It is labeled "A". This is the landing point of the small ball on the inclined plane.