Final answer:
The speed of the ball at the bottom of the window can be found using the principle of conservation of energy. By equating the gravitational potential energy and kinetic energy at the top of the window, we can solve for the velocity. Substituting the given values, the speed of the ball at the bottom of the window is 7.3 m/s.
Step-by-step explanation:
The ball's speed at the bottom of the window can be found using the principle of conservation of energy. At the top of the window, the ball has gravitational potential energy and kinetic energy which can be expressed as:
mgh = 0.5mv² + mgh
where m is the mass of the ball, g is the acceleration due to gravity, h is the height of the window, and v is the velocity of the ball.
Since the ball is falling, the initial velocity is 0 m/s, and the equation can be simplified to:
mgh = 0.5mv²
The mass of the ball cancels out, so we are left with:
gh = 0.5v²
To find the velocity at the bottom of the window, we can solve for v:
v = sqrt(2gh)
Substituting the given values, we have:
v = sqrt(2 * 9.8 m/s² * 3.4 m) = 7.3 m/s
Therefore, the speed of the ball at the bottom of the window is 7.3 m/s.