A ferris wheel is elevated 1 meter above ground. When car reaches the highest point of the ferris wheel it's altitude from ground level is 31 meters. How far away from the center,horizontally, is the car it is at an altitude of 25 meters?
"Ferris wheel is elevated 1 metre above ground"
means that the lowest point is 1 metre above ground. (Draw a sketch to show that).
The highest point is 31 m. above ground, so the diameter is (31-1)=30m, and radius = 30m/2=15m. (Mark that on your sketch).
The centre C is therefore 15+1=16m above ground. (mark centre C on your sketch, draw a radius and mark 15m).
At an altitude of 25m (above ground), it is (25-16)=9m above the centre of the wheel.
Mark the point as A on your sketch. Join C and A and mark radius AC as 15m.
Draw a horizontal radius below A, and drop a perpendicular from A to the horizontal radius, meeting at B.
Mark B on the sketch.
Now triangle ABC is a right triangle, right-angled at B.
AB=9m, AC=15m.
Use Pythagoras theorem to find the horizontal distance between B and C.
BC=√(15²-9²)
= ?
Since when is math (geometry?) called "Cruz"?
12 m
To find the horizontal distance from the center when the car is at an altitude of 25 meters, we can use the concept of a right triangle.
Let's consider the situation:
The distance from the center of the ferris wheel to the car horizontally is represented by the base of the triangle, and we need to find this distance.
The altitude of the car above ground level (vertical distance) is represented by the height of the triangle, which is 25 meters.
Given that the ferris wheel is elevated 1 meter above the ground, we can determine the total altitude of the ferris wheel at its highest point by adding 1 meter to the altitude of the car. Thus, the height of the triangle at the highest point is 31 meters.
Now, we can calculate the horizontal distance using the Pythagorean theorem, which states that the square of the hypotenuse (the longest side of a right triangle) is equal to the sum of the squares of the other two sides.
Since we know the height and the hypotenuse, we can solve for the base (horizontal distance).
Let's label the hypotenuse as c and the base as b.
Using the Pythagorean theorem:
c^2 = b^2 + h^2
Solving for b:
b^2 = c^2 - h^2
Substituting the given values:
b^2 = 31^2 - 25^2
b^2 = 961 - 625
b^2 = 336
To find b, we take the square root of both sides:
b = sqrt(336)
b ≈ 18.33 meters
Therefore, when the car is at an altitude of 25 meters, it is approximately 18.33 meters away from the center horizontally.