Final answer:
The ball's instantaneous speed at the top of its path is zero due to gravity's deceleration. To find the initial velocity, we analyze the ball's motion using kinematic equations, considering the velocity at the bottom of the window, the height of the window, and acceleration due to gravity.
Step-by-step explanation:
When a ball is thrown straight up, at the top of its path its instantaneous speed is zero. This is because gravity has decelerated the ball to a stop before it starts to fall back down. However, solving for the ball's initial velocity when it is thrown past a window requires analyzing its motion using the principles of kinematics.
To determine the ball's initial velocity, we'll first calculate its velocity at the bottom of the window using the distance it travels past the window and the time taken. Then, using this velocity as the final velocity, we'll calculate the initial velocity considering the distance from the ground to the bottom of the window and the acceleration due to gravity. Note that the acceleration of the ball from the instant after it leaves the thrower's hand until the time it hits the ground is directed downwards, towards the center of the Earth, at a constant value of approximately 9.8 m/s2.