a roller coaster moves 85m horizontally, then travels 45m at an angle of 30.0 above the horizontal. What is displacement from its starting point?
Break up the angle into horizontal and vertical parts.
displacement=sqrt(85+horizontal)^2 + (vertical)^2 )
To calculate the displacement from the starting point, we need to determine the total horizontal and vertical distances covered by the roller coaster.
Step 1: Calculate the horizontal distance:
The roller coaster moves 85m horizontally, so its horizontal distance is 85m.
Step 2: Calculate the vertical distance:
The roller coaster travels 45m at an angle of 30.0° above the horizontal. We need to find the vertical component of this distance.
We can use trigonometry to find the vertical distance. The vertical component can be calculated by multiplying the given distance by the sine of the angle.
Vertical distance = 45m * sin(30.0°)
Step 3: Calculate the displacement:
The displacement is the straight-line distance between the starting and ending points.
We can use the Pythagorean theorem to calculate the displacement. The displacement is the square root of the sum of the squares of the horizontal and vertical distances.
Displacement = √(Horizontal distance^2 + Vertical distance^2)
Displacement = √(85m^2 + (45m * sin(30.0°))^2)
Now, let's calculate the displacement:
Displacement = √(85m^2 + (45m * sin(30.0°))^2)