## How Long Would It Take a Skydiver to Reach 180km?
Skydiving is an exhilarating sport that involves jumping from an airplane and freefalling through the air. The time it takes to reach a certain altitude depends on several factors, including the skydiver’s weight, body position, and the air density.
### Factors Affecting Skydiving Time
The following factors can affect the time it takes a skydiver to reach 180 km:
Weight: Heavier skydivers fall faster than lighter skydivers.
Body Position: A skydiver in a flat, belly-down position (known as freefall) experiences less air resistance and falls faster than a skydiver in a more upright position.
Air Density: Air density decreases with altitude. As the skydiver ascends, the air becomes less dense, reducing air resistance and increasing falling speed.
### Calculating Skydiving Time
To determine the time it takes to reach 180km, we need to use the following formula:
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Time = Distance / Velocity
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where:
Time: Time it takes to reach the altitude
Distance: Altitude to be reached (180km)
Velocity: Skydiver’s falling velocity
### Skydiver’s Velocity
The skydiver’s velocity in freefall is affected by weight and air resistance. The relationship between weight, velocity, and air resistance can be expressed using the following formula:
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Velocity = (Weight Gravitational Constant) / Air Resistance
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where:
Gravitational Constant: Constant value of 9.8 m/s²
Air Resistance: Resistance force exerted by the air on the skydiver
### Example Calculation
Let’s assume the skydiver weighs 80kg and is in a freefall position. The air density at the altitude where they start their jump is 1.225 kg/m³.
Calculating Velocity:
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Weight = 80kg
Gravitational Constant = 9.8 m/s²
Air Resistance = (0.5 Air Density Skydiver’s Frontal Area Velocity²)
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We don’t know the skydiver’s frontal area, but we can assume it is 0.6 m².
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Air Resistance = (0.5 1.225 kg/m³ 0.6 m²) Velocity²
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Calculating velocity using numerical methods (e.g., iteration or interpolation) yields a velocity of approximately 50 m/s.
Calculating Time:
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Distance = 180km = 180,000m
Velocity = 50 m/s
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Plugging these values into the time formula:
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Time = 180,000m / 50 m/s
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Result:
It would take a skydiver in freefall weighing 80kg and with a frontal area of 0.6 m² approximately 60 minutes to reach an altitude of 180km.
### Considerations
This is just an approximate calculation. The actual time may vary depending on the specific conditions during the skydive. Additionally, the skydiver would likely use a parachute to slow their descent before reaching 180km.
### Additional Factors
Other factors that can affect skydiving time include:
Equipment: The type of parachute used can affect the rate of descent.
Weather Conditions: Wind speed and direction can affect falling speed.
Experience: More experienced skydivers may be able to control their descent more effectively.
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