A stone is dropped from the root of a building. A person in the building observes that the stone
crosses his window that is 2 meters tall in a time of 0.2 second. How far is the roof from the top of
the window?
hf=hi+vi*t-1/2 g t^2
-2=0+vi*.2-4.8 (.2^2)
so solve for vi, the velocity at the top of the windown. Then,
vf^2=2gh where h is the distance to the roof from the top of windown. Vf is the vi you found above. Solve for h.
To answer this question, we can use the equation of motion for an object in free fall. This equation relates the distance an object travels to its initial velocity, acceleration due to gravity, and time.
Let's break down the problem:
1. The stone is dropped from the roof of a building.
2. The stone crosses the window that is 2 meters tall in a time of 0.2 seconds.
We need to find the distance between the roof of the building and the top of the window. Let's call this distance "d".
Using the equation of motion, we have:
d = (1/2) * g * t^2
Where:
- d is the distance traveled by the object
- g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth)
- t is the time it takes for the object to travel that distance
In this case, the distance traveled is equal to the height of the window, which is 2 meters. And the time it takes for the stone to cross the window is 0.2 seconds.
Substituting the given values into the equation, we have:
2 = (1/2) * 9.8 * 0.2^2
Simplifying this equation, we get:
2 = 0.98 * 0.04
2 = 0.0392
Therefore, the equation is not true. There might be an error in the initial data or calculations. Please double-check and provide the correct information so we can assist you further.