A roller coaster moves 85 m horizontally, then travels 45 m at an angle of 30.0 degrees above the horizontally. what is the displacement from its starting point? use graphical techniques.
horizontal: 85 + 45 cos 30 = ?
vertical: 45 sin 30 = ?
X= sqrt(85^2 + 22.5^2)= 87.9M
To find the displacement from the starting point of the roller coaster, we can break down the motion into horizontal and vertical components.
First, let's calculate the horizontal displacement. The roller coaster moves 85 m horizontally to the right. It then travels 45 m at an angle of 30.0 degrees above the horizontal. To find the horizontal displacement, we add the horizontal distances traveled in both parts.
Horizontal displacement = 85 + 45 cos 30
To find the vertical displacement, we consider the vertical distance traveled in the second part. The roller coaster travels 45 m at an angle of 30.0 degrees above the horizontal. The vertical displacement can be calculated using the sine function.
Vertical displacement = 45 sin 30
To get the total displacement, we combine the horizontal and vertical displacements using vector addition. We can use a graphical technique to visualize the displacement. Plot the horizontal displacement as the x-component and the vertical displacement as the y-component on a coordinate system. Then, draw an arrow connecting the origin (starting point) to the ending point of the vector.
Note: The magnitude and direction of the total displacement can be found using the Pythagorean theorem and trigonometry. However, in this case, we are only interested in the numerical value of the displacement and not its direction.