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Solving Quadratic Equations and River Travel Problems

In this exercise, we explore two distinct problems involving quadratic equations and motion in river travel. The first problem involves calculating the time it takes for an object launched from a height to strike the ground, using its height equation over time. The second problem examines a motorboat's round trip on a river, determining the speed of the current based on the time it takes for the boat to travel upstream and downstream. Solutions require application of algebraic methods and understanding of motion in physics.

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Solving Quadratic Equations and River Travel Problems

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  1. Objective: Solve quadratic equations. Warm up Don’t copy problem 1. An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform. The equation for the object's height s at time t seconds after launch is s, where s is in meters. When does the object strike the ground?

  2. Solve for x.

  3. 3. Don’t copy problem A motorboat makes a round trip on a river 56 miles upstream and 56 miles downstream, maintaining the constant speed 15 miles per hour relative to the water. The entire trip up and back takes 7.5 hours. What is the speed of the current?

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