answer:
To find the initial coordinates of the ball, we need to consider the given information about its initial velocity, angle, and the time it takes to hit the ground.
1. Analyze the horizontal motion:
- The initial velocity has both horizontal and vertical components.
- The initial velocity is given as 9.30 m/s at an angle of 21.0° below the horizontal.
- The horizontal component of the initial velocity can be found using trigonometry: vx = v * cos(θ), where v is the magnitude of the initial velocity and θ is the angle below the horizontal.
- Calculate the horizontal component: vx = 9.30 m/s * cos(21.0°).
2. Analyze the vertical motion:
- The initial vertical position of the ball is y0 above the ground.
- The ball hits the ground 4.00 s later.
- The time of flight can be split into two equal parts: the ascent and descent times. So the time taken for ascent is 4.00 s / 2 = 2.00 s.
- Use the kinematic equation y = y0 + v0y * t + (1/2) * a * t^2, where y is the vertical position, y0 is the initial vertical position, v0y is the vertical component of the initial velocity, t is the time, and a is the acceleration (considering only gravity).
- Plug in the known values: y = 0 (since it hits the ground), y0 = y0, v0y = v * sin(θ), t = 2.00 s, a = -9.8 m/s^2 (acceleration due to gravity).
- Solve the equation for y0.
3. Determine the initial coordinates:
- The initial x-coordinate (xi) is taken as the origin of the coordinates, which is the base of the building.
- The initial y-coordinate (yi) is y0, which represents the vertical position above the ground.
Therefore, the initial coordinates of the ball are xi = 0 (taken as the base of the building) and yi = y0.
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