A roller coaster travels 17.6 m at an angle of
38.0
◦
above the horizontal.
How far does it move horizontally?
Answer in units of m
To find the horizontal distance traveled by the roller coaster, we can use the trigonometric function cosine. The cosine of an angle gives us the ratio of the adjacent side to the hypotenuse in a right triangle.
In this case, the adjacent side represents the horizontal distance traveled, and the hypotenuse represents the total distance traveled. Therefore, the equation can be set up as:
cos(38.0◦) = horizontal distance / total distance
To find the horizontal distance, we rearrange the equation as:
horizontal distance = total distance * cos(38.0◦)
Given that the total distance traveled is 17.6 m, we can calculate the horizontal distance using a scientific calculator or trigonometric table:
horizontal distance = 17.6 m * cos(38.0◦)
Calculating this expression gives us:
horizontal distance = 17.6 m * 0.788
Simplifying further:
horizontal distance ≈ 13.8528 m
Therefore, the roller coaster moves approximately 13.8528 meters horizontally.
To find the horizontal distance traveled by the roller coaster, we need to break down the given information into its horizontal and vertical components.
Given:
Distance traveled by the roller coaster = 17.6 m
Angle above the horizontal = 38.0°
We can use trigonometry to find the horizontal distance. In this case, we will use the cosine function, which relates the adjacent side of a right triangle to the hypotenuse.
cos(angle) = adjacent/hypotenuse
By rearranging the formula, we can solve for the adjacent side:
adjacent = cos(angle) * hypotenuse
In this case, the hypotenuse is the distance traveled by the roller coaster, and the adjacent side represents the horizontal distance we need to find.
Substituting the given values:
adjacent = cos(38.0°) * 17.6 m
Now let's calculate the value using a calculator or a computer:
adjacent = cos(38.0°) * 17.6 m
adjacent ≈ 13.672 m (rounded to three decimal places)
Therefore, the roller coaster moves approximately 13.672 m horizontally.