A roller coaster moves horizontally, then travels 45 m at an angle of 30 degrees above the horizontal. What is its displacement from its starting point?

To find the displacement of the roller coaster from its starting point, we need to break down the given information into horizontal and vertical components.

1. Horizontal Component:
The roller coaster moves horizontally before it starts to travel at an angle. Therefore, its horizontal displacement is 0 m.

2. Vertical Component:
The roller coaster travels 45 m at an angle of 30 degrees above the horizontal. To find the vertical displacement, we can use trigonometry.

The vertical displacement can be calculated using the formula:
displacement = distance * sin(angle)

In this case:
distance = 45 m
angle = 30 degrees

Now, let's substitute the values into the formula:
displacement = 45 m * sin(30 degrees)

Using a calculator:
displacement ≈ 22.5 m

Therefore, the roller coaster's displacement from its starting point is approximately 22.5 meters.

To find the displacement of the roller coaster from its starting point, we need to break down the motion into its horizontal and vertical components.

First, let's consider the horizontal motion. Since it moves horizontally, the horizontal component of its displacement is given by the distance it traveled horizontally. In this case, the roller coaster doesn't change its horizontal position, so the horizontal displacement is 0.

Now, let's consider the vertical motion. The roller coaster travels 45 m at an angle of 30 degrees above the horizontal. To find the vertical component of the displacement, we can use trigonometry.

The vertical displacement (y) can be found by using the formula: y = distance * sin(angle)

Given that the distance is 45 m and the angle is 30 degrees, we can substitute the values into the equation: y = 45 * sin(30)

Using a scientific calculator or any tool that can calculate trigonometric functions, we find that sin(30) = 0.5. Therefore, the vertical displacement (y) is: y = 45 * 0.5 = 22.5 m.

Since there is no horizontal displacement and a vertical displacement of 22.5 m, the overall displacement of the roller coaster from its starting point is 22.5 m straight up.