A roller coaster travels 10.6 m at an angle of
15.0◦ above the horizontal.
How far does it move horizontally?
Answer in units of m.
what is 10.6*cosine15?
10.2388
To find out how far the roller coaster moves horizontally, we need to use the given information about the angle and distance traveled.
The distance traveled at an angle can be split into its horizontal and vertical components. The horizontal component represents the distance traveled in the horizontal direction, while the vertical component represents the distance traveled in the vertical direction.
In this case, the roller coaster travels 10.6 m at an angle of 15.0 degrees above the horizontal.
To find the horizontal component, we can use the trigonometric function cosine (cos). The cosine of an angle is the ratio of the adjacent side to the hypotenuse of a right triangle. In this case, the adjacent side represents the horizontal component, and the hypotenuse represents the distance traveled.
So, we can use the formula:
Horizontal component = Distance traveled × cos(angle)
Plugging in the values:
Horizontal component = 10.6 m × cos(15.0 degrees)
Now, we need to evaluate the cosine of 15.0 degrees. Most calculators have a built-in cosine function that can be used to find the cosine of an angle. Using a calculator, we find:
cos(15.0 degrees) ≈ 0.9659
Substituting this value back into the formula:
Horizontal component = 10.6 m × 0.9659
Now, we can calculate the horizontal component:
Horizontal component ≈ 10.22 m
Therefore, the roller coaster moves approximately 10.22 meters horizontally.