Question
A paratrooper falls to the ground along a diagonal line. His fall begins 2, 795 meters above the ground, and the line he follows has a slope of 6.5. That is, he falls 6.5 meters vertically for every 1 meter he moves across horizontally.
How far horizontally across the ground does he land from his initial position in the sky?
How far horizontally across the ground does he land from his initial position in the sky?
Answers
GPT 3.5
To find the horizontal distance the paratrooper lands from his initial position in the sky, we can use the Pythagorean theorem.
Let x be the horizontal distance the paratrooper lands from his initial position in the sky.
Using the slope formula (slope = rise / run), we can find the vertical distance the paratrooper falls:
6.5 = vertical distance / 1
vertical distance = 6.5 meters
Now, we can use the Pythagorean theorem to find the horizontal distance:
(2,795)^2 = x^2 + (6.5)^2
7,807,025 = x^2 + 42.25
x^2 = 7,807,025 - 42.25
x^2 = 7,806,982.75
x ≈ √7,806,982.75
x ≈ 2,794.03
Therefore, the paratrooper lands approximately 2,794.03 meters horizontally across the ground from his initial position in the sky.
Let x be the horizontal distance the paratrooper lands from his initial position in the sky.
Using the slope formula (slope = rise / run), we can find the vertical distance the paratrooper falls:
6.5 = vertical distance / 1
vertical distance = 6.5 meters
Now, we can use the Pythagorean theorem to find the horizontal distance:
(2,795)^2 = x^2 + (6.5)^2
7,807,025 = x^2 + 42.25
x^2 = 7,807,025 - 42.25
x^2 = 7,806,982.75
x ≈ √7,806,982.75
x ≈ 2,794.03
Therefore, the paratrooper lands approximately 2,794.03 meters horizontally across the ground from his initial position in the sky.