A ball is dropped from the top of an apartment building. A person is on a patio somewhere beneath the top of the apartment building and the person notices the ball takes 0.11 seconds to fall from the top of his patio to the bottom of his patio. The height of his patio is 3.1 meters. If the bottom of the person's patio is 45.5 meters from the ground, or bottom of the building, how high, in meters, is the apartment building? Hint: you must find how far above the top of the patio the ball was dropped and then use that with the other given information related to the heights to find the height of the buildin
To find the height of the apartment building, we need to determine how far above the top of the person's patio the ball was dropped.
First, let's calculate the distance the ball fell from the top to the bottom of the patio. We know that it took 0.11 seconds for this to happen, and the height of the patio is 3.1 meters. We can use the formula for free fall:
d = 0.5 * g * t^2
where d is the distance, g is the acceleration due to gravity (9.8 m/s^2), and t is the time.
Plugging in the values, we get:
3.1 = 0.5 * 9.8 * (0.11)^2
Simplifying the equation, we find:
3.1 = 0.5 * 9.8 * 0.0121
Next, let's solve for the distance the ball fell from the top of the building to the top of the patio. Let's represent this distance as x.
x = 3.1 meters
Now, we can use the given information that the bottom of the person's patio is 45.5 meters from the ground.
Thus, the height of the apartment building is:
x + 45.5 meters
Substituting the value of x, we get:
3.1 + 45.5 = 48.6 meters
Therefore, the height of the apartment building is 48.6 meters.
To find the height of the apartment building, we need to determine the distance the ball traveled from the top to the bottom of the person's patio.
Since the ball took 0.11 seconds to fall from the top to the bottom of the patio, we can use the formula for distance traveled by an object under free fall:
d = 1/2 * g * t^2
Where:
d = distance
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
Substituting the given values, we have:
3.1 = 1/2 * 9.8 * 0.11^2
Simplifying the equation:
3.1 = 0.05 * 9.8 * 0.0121
3.1 = 0.05899
Therefore, the distance the ball traveled from the top to the bottom of the person's patio is approximately 3.1 meters.
To find the height of the apartment building, we need to add this distance to the height of the patio and subtract it from the distance to the ground:
Height of building = Distance to ground - (Distance to ground - Height of patio)
Height of building = 45.5 - (45.5 - 3.1)
Height of building = 45.5 - 42.4
So, the height of the apartment building is approximately 3.1 meters.