please show me how to work out this problem:
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.
the answer is 126 m at (1.0 * 10^1) above the horizontal
please show me all the work that needs to be done to solve this problem , including which formula's to use.thnks:)
can someone pleeeas help me on this?
To solve this problem using graphical techniques, we can break it down into two separate displacements: horizontal displacement and vertical displacement.
1. Horizontal Displacement:
The roller coaster moves 85 m horizontally, so its horizontal displacement is 85 m to the right.
2. Vertical Displacement:
The roller coaster travels 45 m at an angle of 30.0 degrees above the horizontal. To find the vertical displacement, we need to use trigonometry.
First, we find the vertical component of the displacement using the formula:
vertical displacement = horizontal displacement * tan(angle)
Given: horizontal displacement = 45 m and angle = 30.0 degrees.
Using the formula, we can calculate the vertical displacement as follows:
vertical displacement = 45 m * tan(30.0 degrees)
vertical displacement ≈ 25.981 m
Now, we can determine the direction of the vertical displacement. As the angle is above the horizontal, the vertical displacement will be in the upward direction.
3. Finding the Total Displacement:
To find the total displacement, we combine the horizontal and vertical displacements using the Pythagorean theorem.
Total displacement = √(horizontal displacement^2 + vertical displacement^2)
Total displacement = √(85 m^2 + 25.981 m^2)
Total displacement ≈ √(7225 m^2 + 675.827561 m^2)
Total displacement ≈ √(7900.827561 m^2)
Total displacement ≈ 88.843 m
The total displacement magnitude is approximately 88.843 m.
Finally, we can find the direction of the total displacement using trigonometry. As the vertical displacement is positive (upwards) and the horizontal displacement is positive (to the right), we can use the tangent function to find the angle.
angle = arctan(vertical displacement / horizontal displacement)
angle = arctan(25.981 m / 85 m)
angle ≈ 0.305 radians = 17.485 degrees
Since the angle is measured above the horizontal, the total displacement is 88.843 m at an angle of 17.485 degrees above the horizontal.
However, the answer you provided (126 m at 1.0 * 10^1 above the horizontal) seems to have a greater magnitude and a slightly different direction. Please check your calculations and provide further clarification if needed.