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:**1. Understand the Problem**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).**2. Identify Knowns and Unknowns*** **Knowns:** * Horizontal velocity (v_x) = 3.80 m/s * Horizontal distance (x) = 15.0 m * Acceleration due to gravity (g) = 9.81 m/s² (downwards)* **Unknown:** * Vertical distance (y) = ? (This is the height of the window)**3. Choose the Right Equations*** **Horizontal Motion:** Since the horizontal velocity is constant, we can use: x = v_x * t (where t is the time of flight)* **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**4. Solve for Time (t)**Using the horizontal motion equation:t = x / v_xt = 15.0 m / 3.80 m/st ≈ 3.95 s**5. Solve for Vertical Distance (y)**Now, plug the time (t) into the vertical motion equation:y = (1/2) * g * t²y = (1/2) * 9.81 m/s² * (3.95 s)²y ≈ 76.5 m**Answer:**The window is approximately 76.5 meters high.