Question

A Ferris wheel is elevated two meters above the ground. The diameter of the wheel is 30 meters. How far away from the center of the wheel is a car if it reaches the highest altitude?

Answer 1

The horizontal distance from the center of the Ferris Wheel of the car at a 25m altitude from the ground is 12 meters.

Step-by-step explanation:

WORD PROBLEM:

In order to solve the given word problem, lets list down first the Given facts as it will help us organize our thoughts.

Given:

h = Height of Ferris wheel above ground = 1 meter

z1 = height of the car at the highest point of the ferris wheel = 31 meters

z2 = height of the car at 25 meters

Required:

x = horizontal distance of the car when  its distance from the ground is 25 meters = ?

Solution:

The above problem can be solved using pythagorean theorem:

brainly.ph/question/2113315

brainly.ph/question/2576539

Given by:

a² + b² = c²

where:

a is the longer side of the right triangle

b is the shorter side of the right triangle ----> this is X in the problem

c is the length of the hypotenuse  

First we need to determine the diameter  D of the Ferris Wheel. This can be solved through below:

D can be solved through subtracting the height of the Ferris wheel above the ground (h) from the height of the car at the highest point from the ground (z1)

Thus;

D = z1 - h

D = 31 - 1

D = 30 meters ; This is the total diameter of the of the Ferris Wheel.

Since we now have the diameter we can now have the radius of the Ferris wheel:

r = D ÷ 2

r = 30 ÷ 2

r = 15 m

Since we are given that the altitude of 25 m (z2), and we are 1 meter (h) above ground, the altitude is 24 m from the lowest point of the Ferris wheel.

Thus:

z2 - h = 25 - 1 =24 m

If we reference it from the center,  

24 m -15 m = 9m = a

9m is the vertical distance of the Ferris wheel at z2 from the center of the Ferris Wheel.

Using the Pythagorean Theorem:

a² + x² = r²

9² + x² = 15²

x² = 15²- 9²

x² = 15²- 9²

x² = 225 -81

x = 

x = 12

Thus;

The horizontal distance from the center of the Ferris Wheel of the car at a 25m altitude from the ground is 12 meters.