Final answer:
To find the ball's initial velocity, calculate its speed at the bottom of the window and then use the kinematic equation to solve for initial velocity from the ground to the bottom of the window considering the distance and the acceleration due to gravity.
Step-by-step explanation:
To determine the initial velocity of the ball, we have to consider two stages of motion separately: motion passing by the window, and motion from the ground to the bottom of the window.
First, we will find the velocity of the ball as it passes the bottom of the window. We know the ball takes 1.30 s to pass a 2.00 m high window, which implies it has a constant speed while passing the window because acceleration due to gravity does not affect the distance covered in a negligibly small time interval. This velocity (Vbottom window) can be found by distance over time: Vbottom window = 2.00 m / 1.30 s = 1.54 m/s (approximately).
Next, we need to find the velocity of the ball at the moment it reached the bottom of the window in its ascent. For this, we will consider the distance from the ground to the bottom of the window (7.50 m) and use the kinematic equation V2 = U2 + 2as, where V is the final velocity, U is the initial velocity, a is the acceleration (negative due to gravity, which is -9.81 m/s2), and s is the distance. We can solve for U (the initial velocity) once we have V (which is the velocity at the bottom of the window we just calculated) and knowing that a = -9.81 m/s2 and s = 7.50 m.
Therefore, V2 = U2 + 2(-9.81)(7.50). Plugging in V = 1.54 m/s (from the first part), we get U2 = V2 - 2(9.81)(7.50). Solving this gives us the initial velocity U, which is the value we are looking for to answer this question.