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:<br /><br />1. Calculate the time it takes for the ball to fall vertically:<br /> - The ball is thrown horizontally, so its initial vertical velocity is 0 m/s.<br /> - The ball falls under the influence of gravity, so we can use the equation for free fall: \( s = \frac{1}{2} g t^2 \), where \( s \) is the vertical distance (7.5 m), \( g \) is the acceleration due to gravity (approximately 9.8 m/s²), and \( t \) is the time.<br /> - Rearranging the equation to solve for \( t \), we get \( t = \sqrt{\frac{2s}{g}} \).<br /> - Plugging in the values, we get \( t = \sqrt{\frac{2 \times 7.5}{9.8}} \approx 1.29 \) seconds.<br /><br />2. Calculate the initial speed of the ball:<br /> - The ball travels horizontally for the same amount of time as it falls vertically.<br /> - We can use the equation for horizontal motion: \( s = v_0 t \), where \( s \) is the horizontal distance (9.5 m), \( v_0 \) is the initial speed, and \( t \) is the time.<br /> - Rearranging the equation to solve for \( v_0 \), we get \( v_0 = \frac{s}{t} \).<br /> - Plugging in the values, we get \( v_0 = \frac{9.5}{1.29} \approx 7.36 \) m/s.<br /><br />Therefore, the initial speed of the ball was approximately 7.36 m/s.