for safety reasons , anyone parasailing behind a boat needs to stay at least 25 feet away from the back of the boat.
if you were parasailing using a 250 foot rope , how far from the boat would you be if you were 100 feet high in the air ? round to the nearest tenth.
what is the maximum safe height staying at least 25 feet away from the boat to which you could rise while parasailing with 250 foot rope? round to the nearest tenth.
if you wanted the maximum height you could sail at to be limited to 50 feet while coming as close as is safe to the boat , how long of a rope should you use ? round to the nearest tenth.please help me!!!!!
as usual, draw a diagram.
(a) x^2 + 100^2 = 250^2
(b) 25^2 + x^2 = 250^2
(c) 25^2 + 50^2 = x^2
To calculate how far from the boat you would be when parasailing 100 feet high with a 250-foot rope, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the height you are parasailing is one side (100 feet), and the distance from the boat to you is another side (let's call it x feet). The hypotenuse will be the length of the rope (250 feet).
So, using the Pythagorean theorem, we have:
x^2 + 100^2 = 250^2
Simplifying this equation, we get:
x^2 + 10,000 = 62,500
Subtracting 10,000 from both sides:
x^2 = 52,500
Taking the square root of both sides:
x ≈ √52,500 ≈ 229.13 feet
Therefore, you would be approximately 229.13 feet away from the boat when parasailing 100 feet high with a 250-foot rope.
To calculate the maximum safe height you can rise while staying at least 25 feet away from the boat, you need to subtract 25 feet from the length of the rope. So, the maximum safe height would be 250 - 25 = 225 feet.
Now, let's calculate the length of the rope needed if you want to limit your maximum height to 50 feet while staying as close as possible to the boat.
Again, using the Pythagorean theorem, we have:
x^2 + 50^2 = (25 + 50)^2 = 75^2
Simplifying this equation:
x^2 + 2,500 = 5,625
Subtracting 2,500 from both sides:
x^2 = 3,125
Taking the square root of both sides:
x ≈ √3,125 ≈ 55.90 feet
Therefore, you would need a rope length of approximately 55.90 feet to limit your maximum height to 50 feet while staying as close as possible to the boat.