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Step 1
I'll solve this problem step by step, following the LaTeX formatting guidelines precisely.

Problem: A 0.500 kg ball is thrown vertically upward with an initial velocity of 20.0 m/s from a height of 1.50 m. Calculate the maximum height reached by the ball.

Step 2
: Identify the Known Information

- Acceleration due to gravity ($$g$$) = $$-9.80 \text{ m/s}^{2}
- Initial velocity (v_{0}) = 20.0 \text{ m/s}

Final Answer

Key Insights: - The ball starts at 1.50 m and gains additional height due to its initial upward velocity - Gravitational acceleration reduces the ball's velocity until it reaches zero at the peak - The maximum height depends on both initial height and initial velocity