A boy drops a 0.50kg rock from a 22m high bridge into a river below.
a) Using the river as a reference point, what is the initial potential energy of the rock?
b) What is the final speed of the rock just before it hits the water?
a) The initial potential energy of the rock can be calculated using the formula: potential energy = mass × gravity × height.
Given that the mass of the rock is 0.50 kg, the acceleration due to gravity is approximately 9.8 m/s^2, and the height of the bridge is 22m, we can substitute these values into the formula:
Potential energy = 0.50 kg × 9.8 m/s^2 × 22 m = 107.8 Joules
Therefore, the initial potential energy of the rock is 107.8 Joules.
b) To calculate the final speed of the rock just before it hits the water, we can use the law of conservation of energy. The initial potential energy will be converted into kinetic energy just before hitting the water. The formula for kinetic energy is: kinetic energy = 0.5 × mass × velocity^2.
Using the initial potential energy (107.8 J) and the mass of the rock (0.50 kg), we can set up the equation:
107.8 J = 0.5 × 0.50 kg × velocity^2
Simplifying the equation:
107.8 J = 0.25 kg × velocity^2
Dividing both sides of the equation by 0.25 kg:
431.2 J/kg = velocity^2
Taking the square root of both sides of the equation to solve for velocity:
velocity = √(431.2 J/kg) ≈ 20.8 m/s
Therefore, the final speed of the rock just before it hits the water is approximately 20.8 m/s.