1. **Stating the problem:** We want to find the height of a ball when it reaches the hoop. 2. **Formula used:** The height $h$ of a ball thrown upwards with initial velocity $v_0$ from initial height $h_0$ at time $t$ is given by the equation: $$h = h_0 + v_0 t - \frac{1}{2} g t^2$$ where $g$ is the acceleration due to gravity (approximately 9.8 m/s²). 3. **Important rules:** - The height depends on the time $t$ when the ball reaches the hoop. - We need to know or calculate the time $t$ at which the ball reaches the horizontal position of the hoop. 4. **Intermediate work:** - If the horizontal distance to the hoop and the horizontal velocity are known, calculate $t$ by dividing distance by horizontal velocity. - Substitute $t$ into the height formula. 5. **Explanation:** - First, find the time $t$ when the ball reaches the hoop horizontally. - Then plug $t$ into the height formula to find the vertical position (height) at that time. 6. **Final answer:** The height of the ball when it reaches the hoop is $$h = h_0 + v_0 t - \frac{1}{2} g t^2$$ where $t$ is the time to reach the hoop horizontally.