Final answer:
To predict the displacement of a roller coaster that moves horizontally and at an angle, we can break down the motion into horizontal and vertical components. Using the Pythagorean theorem, we can find the displacement from the starting point. The predicted displacement is 90.85 m.
Step-by-step explanation:
Problem:
A roller coaster moves 85 m horizontally and then travels 45 m at an angle of 30.0° above the horizontal. Use graphical techniques to predict its displacement from its starting point.
Answer: To solve this problem, we can break down the motion into horizontal and vertical components. The horizontal component is 85 m, and the vertical component is 45 m * sin(30.0°). Using this information, we can use the Pythagorean theorem to find the displacement from the starting point. The displacement is given by:
displacement = sqrt((horizontal component)^2 + (vertical component)^2) Substituting the given values:
displacement = sqrt((85 m)^2 + (45 m * sin(30.0°))^2) Simplifying, we find:
displacement = sqrt(7225 m^2 + 1012.5 m^2) = sqrt(8237.5 m^2) = 90.85 m Therefore, the predicted displacement from its starting point is
90.85 m.
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