A roller coaster moves 85 m horizontally, then travels 45 m at an angle of 30.0 degrees above the horizontal. What is its displacement from its starting point? Use graphical techniques.
How would I solve this?
Solve it my adding the vector displacement of the first step (which is horizontal and in the "x" direction) to the vector displacement of the second step (partly horizontal and partly vertical - resulting in a displacement in both x and y direction).
Yeah but I think I did that and I got it where the hypotenuse was 45 but that is not the longest side.
This is not a triangle problem. There is no hypotenuse. You add a vector horizontal line to another vector inclined at an angle to the horizontal
To solve this problem using graphical techniques, you will need to create a scale diagram of the roller coaster's movement. Here are the steps:
Step 1: Draw a horizontal line to represent the 85 m of horizontal movement. Label it as the "x" direction.
Step 2: From the end of the horizontal line, draw a line at an angle of 30.0 degrees above the horizontal. This line represents the 45 m of movement at an angle.
Step 3: The endpoint of the angled line represents the displacement of the roller coaster from its starting point. You can measure the distance of this displacement from the starting point using a ruler or measuring tape.
Step 4: This measured distance will be the magnitude of the displacement. To determine the direction of the displacement, you can use a protractor to measure the angle between the horizontal line and the displacement line.
Step 5: Use vector addition to find the resulting displacement. Take the horizontal displacement of 85 m as the x-component and the vertical displacement as the y-component. Find the resultant displacement by calculating the square root of the sum of the squares of the x and y components. To find the angle of the displacement, use the inverse tangent function to determine the angle between the displacement and the horizontal direction.
By following these steps, you can determine the magnitude and direction of the roller coaster's displacement from its starting point using graphical techniques.