A coin rolls along the top of a 4.33 meter high desk with a constant velocity. It reaches the edge of the desk and hits the ground +0.15 meter from the edge of the desk. What was the velocity of the coin at it rolled across the desk?
To determine the velocity of the coin as it rolled across the desk, we can use the principle of conservation of energy.
1. First, calculate the potential energy the coin had at the top of the desk, just before it reached the edge. The potential energy (PE) is given by the formula: PE = m * g * h, where m is the mass of the coin, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height of the desk (4.33 meters in this case).
2. Next, calculate the total energy (E) of the system just before the coin hits the ground. The total energy is the sum of the potential energy and the kinetic energy of the coin. Since the coin is moving at a constant velocity, it has no change in kinetic energy. Therefore, E = PE.
3. Now, calculate the horizontal distance the coin traveled from the edge of the desk to the point where it hit the ground. In this case, it is 0.15 meters.
4. Since the only force acting on the coin is gravity, its potential energy is converted into kinetic energy as it falls. Therefore, the potential energy at the top of the desk is equal to the kinetic energy when it hits the ground. This can be expressed as m * g * h = (1/2) * m * v², where v is the velocity of the coin.
5. Now, solve the equation for v. Cancel out the mass of the coin from both sides of the equation and rearrange the equation to solve for v: v = √(2 * g * h).
6. Substitute the values of the acceleration due to gravity (g = 9.8 m/s²) and the height of the desk (h = 4.33 m) into the equation to calculate the velocity of the coin: v = √(2 * 9.8 * 4.33).
7. Evaluate the expression to find the final answer: v = √(85.72) ≈ 9.26 m/s.
Therefore, the velocity of the coin as it rolled across the desk was approximately 9.26 m/s.