Calculating Displacement of Roller Coaster Motion

In summary, the roller coaster moves a total of 351 ft horizontally and rises 150 ft vertically at an angle of 27.5o above the horizontal. It then travels an additional 150 ft at an angle of 38.2o below the horizontal. The total displacement from the starting point is approximately 368.7 ft at an angle of 3.1o above the horizontal.
  • #1
gadawg90
18
0
A roller coaster moves 201 ft horizontally, then rises 150 ft at an angle of 27.5o above the horizontal. It then travels 150 ft at an angle of 38.2o below the horizontal. What is the magnitude of its displacement from the starting point at the end of this movement? What is the angle relative to the horizontal of this displacement? Use positive values for angles above and negative values for angles below the horizontal.

I think you ahve to split this up into its x and y components? help would be awesome.
 
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  • #2
gadawg90 said:
I think you ahve to split this up into its x and y components? help would be awesome.

Yes! Figure out the total horizontal displacement & total vertical displacement. Then the answer will come easily.
 
  • #3
right i understand i need to find those, but can someone start me off in the right direction..
 
  • #4
Use the head to tail method of vector addition to make it easier to get at an answer.
 
  • #5
So the roller coaster moves 201 ft initially, so that's x=201, y=0. Then it moves 150 ft at an angle of 27.5o above the horizontal, so x=201+150*cos(27.5), y=0+150sin(27.5). Do the same with the rest of the ride.
 

1. How do you calculate the displacement of a roller coaster?

The displacement of a roller coaster can be calculated by subtracting the initial position from the final position. This can be represented as: Displacement = Final Position - Initial Position.

2. What is the formula for calculating displacement?

The formula for calculating displacement is: Displacement = Final Position - Initial Position.

3. How do you determine the initial and final positions of a roller coaster?

The initial position of a roller coaster can be determined by measuring the distance from the starting point of the ride, while the final position can be determined by measuring the distance from the ending point of the ride.

4. Can displacement be negative?

Yes, displacement can be negative if the final position is less than the initial position. This means that the object has moved backwards or in the opposite direction.

5. How is displacement different from distance?

Distance is the total length of the path traveled by an object, while displacement is the straight-line distance between the initial and final positions. Distance does not take into account the direction of motion, whereas displacement does.

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