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Decomposing Vectors & Solving Real-World Motion Problems

This content explores the decomposition of vectors using examples such as finding the components of vectors that are perpendicular to each other. It also covers real-world applications, including calculating the speed and directional vectors of an aircraft in various wind conditions, and determining the forces acting on a vehicle parked on a slope. These examples help illustrate the practical use of vector decomposition in physics and engineering, showcasing how vectors relate to motion and forces in everyday scenarios.

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Decomposing Vectors & Solving Real-World Motion Problems

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  1. 8.5 Vectors more examples

  2. Given v = 3i + 6j and w = -2i + 3j Find the decomposition of v into two vectors that are perpendicular to each other. v1 = ( v • w / ll w ll2) * (w) v1 = 12 / 13 (w) = (-24/13) i + (36/13)j v2 = v – v1 = (51/13) i + (42/13) j

  3. Word problems: A DC 10 jumbo jet maintains an airspeed of 550 miles per hour in a southwesterly direction. The velocity of the jet steam is a constant 80 mph from the west. Find the actual speed and direction of the aircraft.

  4. Ex 2 A Toyota Sienna weight of 5300 pounds is parked on a street with a slope of 8º. Find the force required to keep the Sienna from rolling down the hill. What is the force perpendicular to the hill?

  5. An airplane has airspeed of 600 km/hr bearing S30E.The wind velocity is 40 km/hr in the direction of S45E. Find the resultant vector representing the path of the plane relative to the ground. What is the ground speed of the plane? What is its direction?

  6. HW pg 637 20 – 28 even

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