A man weighs 180lb on the surface of the earth. Computer his weight in an airplane flying at an elevation of 30000ft.
This is the challenging question to me am in need of an answer.
since F is inversley proportional to distance squared,
if the earth's radius is R feet, then it will be
R^2/(R+30000)^2 * 180
To calculate the weight of a man in an airplane flying at an elevation of 30000ft, you need to take into consideration the change in gravitational force at that altitude.
Step 1: Determine the acceleration due to gravity at 30000ft.
The acceleration due to gravity decreases with increasing altitude. At sea level, the acceleration due to gravity is approximately 32.174 ft/s^2. You can use the following formula to calculate the acceleration due to gravity at 30000ft:
g' = g * (R^2 / (R + h)^2)
Where:
g' = acceleration due to gravity at 30000ft
g = acceleration due to gravity at sea level (32.174 ft/s^2)
R = radius of the Earth (which is approximately 3959 miles or 20,926,706.8 ft)
h = altitude in feet (30000ft)
Step 2: Calculate the weight of the man at 30000ft.
The weight of an object can be calculated using the formula:
weight = mass * acceleration due to gravity
Assuming the man's mass remains constant, you can calculate his weight at 30000ft by multiplying his mass by the acceleration due to gravity at that altitude.
It's important to note that this calculation assumes the airplane is at a steady altitude and not accelerating or decelerating.
Let's calculate the weight of the man at 30000ft:
Step 1:
g' = 32.174 ft/s^2 * (20,926,706.8 ft^2 / (20,926,706.8 ft + 30,000 ft)^2)
g' ≈ 32.174 ft/s^2 * 0.9975 ≈ 32.07 ft/s^2
Step 2:
weight at 30000ft = mass * g'
weight at 30000ft = 180 lb * 32.07 ft/s^2
So, the weight of the man in the airplane flying at an elevation of 30000ft is approximately 5772.6 lb-ft/s^2, which is approximately 5772.6 lb.
To calculate the weight of the man in an airplane flying at an elevation of 30,000 feet, we need to consider the effect of gravity on his body.
First, let's understand that weight is a force resulting from the acceleration due to gravity acting on an object's mass.
At the surface of the Earth, the acceleration due to gravity is approximately 9.8 m/s^2. However, as we ascend in altitude, the acceleration due to gravity decreases slightly.
To calculate the weight of the man in the airplane, we can use the formula:
Weight = Mass * Acceleration due to gravity
Given that the man weighs 180 lb on the surface of the Earth, we need to convert his weight to mass.
To convert weight in pounds to mass in kilograms, we can use the conversion factor: 1 lb = 0.453592 kg.
So, the man's mass would be:
Mass = 180 lb * 0.453592 kg/lb ≈ 81.65 kg
Now, we need to adjust the value of the acceleration due to gravity at an elevation of 30,000 feet.
At higher altitudes, the acceleration due to gravity decreases due to the increasing distance from the Earth's center. It is approximately 9.81 m/s^2 at sea level but gradually decreases as altitude increases.
To find the acceleration due to gravity at an elevation of 30,000 feet, we can use a mathematical model:
Acceleration due to gravity at altitude = 9.81 m/s^2 * (1 - (2 * altitude) / (Earth's radius))
The Earth's radius is approximately 6,371,000 meters.
Plugging in the values:
Acceleration due to gravity at 30,000 feet ≈ 9.81 m/s^2 * (1 - (2 * 9,144 m) / (6,371,000 m))
≈ 9.81 m/s^2 * (1 - 0.00286134)
≈ 9.81 m/s^2 * 0.99713866
≈ 9.756 m/s^2
Finally, we can calculate the man's weight in the airplane:
Weight = Mass * Acceleration due to gravity at altitude
Weight = 81.65 kg * 9.756 m/s^2
Weight ≈ 796.30 N
Therefore, the approximate weight of the man in the airplane flying at an elevation of 30,000 feet is about 796.30 Newtons.