Brica throws a ball out of a window with a horizontal speed of 3.80m/s If the ball hit the ground 15.0 m away, how high up is the window?

Here's how to solve this projectile motion problem:<br /><br />**1. Understand the Problem**<br /><br />We're dealing with two-dimensional motion. Horizontally, the ball moves at a constant speed. Vertically, it accelerates downwards due to gravity. We need to find the vertical distance (the height of the window).<br /><br />**2. Identify Knowns and Unknowns**<br /><br />* **Knowns:**<br /> * Horizontal velocity (v_x) = 3.80 m/s<br /> * Horizontal distance (x) = 15.0 m<br /> * Acceleration due to gravity (g) = 9.81 m/s² (downwards)<br /><br />* **Unknown:**<br /> * Vertical distance (y) = ? (This is the height of the window)<br /><br />**3. Choose the Right Equations**<br /><br />* **Horizontal Motion:** Since the horizontal velocity is constant, we can use: x = v_x * t (where t is the time of flight)<br /><br />* **Vertical Motion:** We can use the following equation for vertical displacement: y = v_y0 * t + (1/2) * g * t² Since the ball is thrown horizontally, the initial vertical velocity (v_y0) is 0. This simplifies the equation to: y = (1/2) * g * t²<br /><br />**4. Solve for Time (t)**<br /><br />Using the horizontal motion equation:<br /><br />t = x / v_x<br />t = 15.0 m / 3.80 m/s<br />t ≈ 3.95 s<br /><br />**5. Solve for Vertical Distance (y)**<br /><br />Now, plug the time (t) into the vertical motion equation:<br /><br />y = (1/2) * g * t²<br />y = (1/2) * 9.81 m/s² * (3.95 s)²<br />y ≈ 76.5 m<br /><br />**Answer:**<br /><br />The window is approximately 76.5 meters high.<br />