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Understanding Square Roots: Calculating Speeds for Amusement Park Rides

This guide explains how to evaluate square roots and apply them in real-life scenarios, specifically in amusement park rides. Using examples, we demonstrate how to find the speed required to keep riders securely against the ride wall by leveraging the radius of the ride. You'll learn how to use a calculator for approximating square roots to the nearest tenth and apply mathematical models to solve practical problems in physics related to circular motion.

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Understanding Square Roots: Calculating Speeds for Amusement Park Rides

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  1. b. 8 SOLUTION Keystrokes Display Answer a. [ ] 56.25 – – 7.5 7.5 b. [ ] 8 2.828427125 2.8 c. [ ] 1256 – – 35.44009029 35.4 Example 5 Using a Calculator Evaluate the square root. Round to the nearest tenth if necessary. a. c. – 56.25 – 1256

  2. r r SOLUTION Write model for speed of the ride. 2.61 Substitute 2.61 for r. s s 4.95 4.95 4.95 = = = Example 6 Using a Square Root in Real Life AMUSEMENT PARKS The model gives the speed needed to keep riders pinned to the wall of an amusement park ride. In the model, s is the speed (in meters per second) and r is the radius of the ride (in meters). Find the speed necessary to keep riders pinned to the wall of a ride that has a radius of 2.61 meters.

  3. ANSWER Multiply. 8.019 = The speed should be about 8 meters per second. ( ) 1.62 Example 6 Using a Square Root in Real Life Approximate the square root using a calculator. 4.95 ≈

  4. Guided Practice 236 15.4 ANSWER 11. WHAT IF?In Example 6, what is the speed necessary to keep riders pinned to the wall of a ride that has a radius of 3.56 meters? Round your answer to the nearest tenth of a meter per second. 9.3 m per sec ANSWER for Examples 5 and 6 10. Use a calculator to evaluate to the nearest tenth.

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