Working with time and dropping from a specified height

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In summary, the conversation is about a person struggling to find the correct formula to solve a math problem involving a construction worker dropping a paint drop from a rafter 225 feet above ground. The person knows the distance, initial velocity, and acceleration, but needs to find the time it takes for the paint to hit the ground. They are then provided with a formula to solve the problem.
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averyjedwards2
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hello there! I've been working on math for a while, and on y math homework there's a specific question that i just don't know of the correct formula to solve it. i can do algebra quite well, i just can't recall what this specific formula may be. here is my question:
A construction worker is working on the roof of a building. a drop of paint falls from a rafter that is 225 feet about the ground. after how many seconds does the paint hit the ground?
 
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If we ignore drag, then a freefalling body near the surface of the Earth experiences a constant acceleration of about 32.2 ft/s/s. So, we know the distance $d$ (225 ft), the initial velocity $v_0 = 0$, and the acceleration $a$, and we need the time to cover that distance. A useful formula is thus:

\(\displaystyle t=\sqrt{2ad+v_0^2}\)

Can you proceed?
 

FAQ: Working with time and dropping from a specified height

How does the height from which an object is dropped affect the time it takes to reach the ground?

The height from which an object is dropped does not affect the time it takes to reach the ground, as long as there is no air resistance. This is because the acceleration due to gravity is constant and independent of the object's starting point.

Can the weight or mass of an object affect the time it takes to fall from a specified height?

No, the weight or mass of an object does not affect the time it takes to fall from a specified height. The only factors that affect the time are the acceleration due to gravity and the height from which the object is dropped.

How does air resistance impact the time it takes for an object to fall from a specified height?

Air resistance can have a significant impact on the time it takes for an object to fall from a specified height. As the object falls, air resistance will increase, causing the object to eventually reach a terminal velocity. This means that the object will stop accelerating and its downward velocity will remain constant. Therefore, air resistance can make the object take longer to reach the ground.

Is there a formula to calculate the time it takes for an object to fall from a specified height?

Yes, the formula to calculate the time it takes for an object to fall from a specified height is t = √(2h/g), where t is the time in seconds, h is the height in meters, and g is the acceleration due to gravity (9.8 m/s²).

How can the time it takes for an object to fall from a specified height be affected by external factors?

The time it takes for an object to fall from a specified height can be affected by external factors such as air resistance, wind, and the shape and weight distribution of the object. These factors can change the object's terminal velocity and therefore impact the time it takes to reach the ground. Additionally, if the object is dropped from a height above sea level, the acceleration due to gravity may vary slightly, which can also affect the time it takes to fall.

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