Vectors Solving Mathematically Vectors If two vectors are

Vectors If two vectors are arranged at 90º, we can use mathematics to make

Vectors Make a “sketch” of the problem. This does not need to be made

Vectors Procedure: 1) Write equation. 40 m a 2 + b 2 = c

Vectors Procedure to find Direction: 1) Write an equation. 40 m (opp) tan Θ

Vectors 40 m 30 m Θ = 31º R = 50 m Displacement (R)

Vectors Note the procedure described in the previous example. To receive full credit on

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Vectors Solving Mathematically

Vectors If two vectors are arranged at 90º, we can use mathematics to make our lives somewhat easier. For example: A student walks 30 m north than 40 m east. What is the students displacement?

Vectors Make a “sketch” of the problem. This does not need to be made to scale. It is only for your reference. 40 m Looking at our sketch we see our two vectors make a right triangle. 90º 30 m R=? This allows us to us the Pythagorean Theorem and SOH CAH TOA to solve.

Vectors Procedure: 1) Write equation. 40 m a 2 + b 2 = c 2 2) Sub in with units. (30 m)2 + (40 m)2 = c 2 30 m Θ R = 50 m 3) Solve in with units. c = 50 m However, we are not done. Since vectors have magnitude and direction, we must include a direction.

Vectors Procedure to find Direction: 1) Write an equation. 40 m (opp) tan Θ = opp / adj 2) Sub in with units. tan Θ = 40 m / 30 m (adj) Θ R = 50 m 3) Solve in with units. Θ = 31º Now we have both magnitude and direction, so we can properly call out the displacement.

Vectors 40 m 30 m Θ = 31º R = 50 m Displacement (R) = 50 m @ 31º east of north

Vectors Note the procedure described in the previous example. To receive full credit on short answer questions you must perform the following steps: 1) Write an equation. 2) Sub in with units. 3) Solve in with units.