The height of the Empire State building is 318.00 meters. A pebble is dropped from the top of the building, what is the stones velocity just before it strikes the ground?
final KE=initial PE
1/2 m v^2=mgh
v=sqrt(2*9.8*318) ignoring air friction, which is significant.
To determine the stone's velocity just before it strikes the ground, we can use the principles of kinematics and the equation for free-falling motion. The key parameters we need are the height of the building (h), the acceleration due to gravity (g), and the unknown velocity of the stone (v).
Here's how we can calculate the stone's velocity:
1. Take note of the given information:
- Height of the Empire State Building: h = 318.00 meters
- Acceleration due to Gravity: g = 9.8 m/s² (approximately, on the surface of the Earth)
2. Use the equation of motion for free-falling objects:
- Δy = v₀t + 0.5gt²
- Here, Δy represents the change in vertical position (height), v₀ is the stone's initial velocity (which is 0 m/s since it is dropped), t is the time taken for the stone to fall, and g is the acceleration due to gravity.
3. We want to find the final velocity of the stone (v), so we'll rearrange the equation:
- h = 0.5gt²
- Rearrange to solve for t:
t = √(2h/g)
4. Substitute the given values into the equation:
- t = √(2 * 318.00 / 9.8)
- t ≈ 8.02 seconds (rounded to two decimal places)
5. Now that we know the time it takes for the stone to fall, we can find its velocity just before it strikes the ground using the equation:
v = gt
- Substitute the values:
v ≈ 9.8 m/s² * 8.02 s ≈ 78.80 m/s
Therefore, the stone's velocity just before it strikes the ground is approximately 78.80 m/s.