7. A ball is thrown horizontally from the roof of a build-ing 7.5 m tall and lands 9.5 m from the base . What was the ball's initial speed?

To find the initial speed of the ball, we can use the following steps:1. Calculate the time it takes for the ball to fall vertically: - The ball is thrown horizontally, so its initial vertical velocity is 0 m/s. - The ball falls under the influence of gravity, so we can use the equation for free fall: , where is the vertical distance (7.5 m), is the acceleration due to gravity (approximately 9.8 m/s²), and is the time. - Rearranging the equation to solve for , we get . - Plugging in the values, we get seconds.2. Calculate the initial speed of the ball: - The ball travels horizontally for the same amount of time as it falls vertically. - We can use the equation for horizontal motion: , where is the horizontal distance (9.5 m), is the initial speed, and is the time. - Rearranging the equation to solve for , we get . - Plugging in the values, we get m/s.Therefore, the initial speed of the ball was approximately 7.36 m/s.