Understanding the Physics
* Gravity: The ball is affected by gravity, which causes it to decelerate as it moves upward. The acceleration due to gravity is approximately -9.8 m/s² (negative since it acts downward).
* Energy Conservation: We can use the principle of conservation of energy to solve this. The total mechanical energy (potential energy + kinetic energy) of the ball remains constant throughout its motion.
Calculations
1. Potential Energy at Maximum Height:
* The ball's potential energy (PE) at its highest point is: PE = mgh, where:
* m = mass (0.300 kg)
* g = acceleration due to gravity (9.8 m/s²)
* h = height (10.0 m)
* PE = (0.300 kg)(9.8 m/s²)(10.0 m) = 29.4 J
2. Kinetic Energy at Release:
* At the moment of release, the ball has only kinetic energy (KE). Since energy is conserved, the KE at release equals the PE at the highest point: KE = 29.4 J
3. Initial Velocity:
* KE = (1/2)mv², where v is the initial velocity.
* 29.4 J = (1/2)(0.300 kg)v²
* Solving for v: v = √(2 * 29.4 J / 0.300 kg) ≈ 14.0 m/s
Therefore:
* The initial velocity of the ball when it was thrown upward is approximately 14.0 m/s.
Additional Information
* Time to Reach Maximum Height: You could also calculate the time it takes for the ball to reach its maximum height using kinematic equations.
* Total Time in the Air: Since the motion is symmetrical, the total time the ball is in the air is twice the time it takes to reach its maximum height.
