Final answer:
The ball's initial speed, calculated using the law of conservation of energy, and considering the maximum height of 3.3 meters, is approximately 8.0 m/s.
Step-by-step explanation:
To determine the ball's initial speed using the law of conservation of energy, we must equate the ball's gravitational potential energy at its maximum height with its kinetic energy at the point of release. The potential energy (PE) can be expressed as PE = mgh, where m is the mass of the ball, g is the acceleration due to gravity (9.8 m/s2), and h is the maximum height. The kinetic energy (KE) is expressed as KE = 1/2 mv2, where v is the initial velocity of the ball.
Setting the potential energy at the maximum height equal to the kinetic energy at the start, we get mgh = 1/2 mv2. The mass cancels out, which simplifies to gh = 1/2 v2. To find the initial speed v, we rearrange the formula: v = sqrt(2gh). Plugging in the values, v = sqrt(2 * 9.8 * 3.3), which calculates to approximately 8.0 m/s.