Roller coaster displacement physics problem

[kiss the shrew]

here's the question
a roller coaster moves 85m horizontally, then travels 45m at an angle of 30.0 degrees above the horizontal. What is its displacement from its starting point?

can anybody help me do this?

 

[Andrew Mason]

here's the question
a roller coaster moves 85m horizontally, then travels 45m at an angle of 30.0 degrees above the horizontal. What is its displacement from its starting point?

can anybody help me do this?

To add displacement vectors, add their horizontal and vertical components and then use the Pythagorean theorem to determine the length.

AM

 

[kyle8921]

Sure, I can help you with this problem. In order to calculate the displacement of the roller coaster, we need to use the formula for vector addition. This formula states that the displacement (d) is equal to the square root of the sum of the squares of the horizontal displacement (dx) and vertical displacement (dy). In this case, the horizontal displacement is 85m and the vertical displacement is 45m. We also need to take into account the angle of 30.0 degrees, which is the direction of the displacement.

Using trigonometry, we can calculate the horizontal and vertical components of the displacement. The horizontal component (dx) can be found by multiplying the total displacement (d) by the cosine of the angle (30.0 degrees). So, dx = d * cos(30.0) = 85m * cos(30.0) = 73.6m. Similarly, the vertical component (dy) can be found by multiplying the total displacement (d) by the sine of the angle (30.0 degrees). So, dy = d * sin(30.0) = 85m * sin(30.0) = 42.5m.

Now, we can use the formula for vector addition to calculate the total displacement (d). d = √(dx² + dy²) = √(73.6m² + 42.5m²) = √(5395.36m² + 1806.25m²) = √7201.61m² = 84.9m. Therefore, the displacement of the roller coaster from its starting point is 84.9m.

I hope this helps you understand the displacement of the roller coaster. If you have any further questions, please let me know. Keep up the good work!