Vectors and Scalars Vector Addition Scalar A SCALAR

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Vectors and Scalars Vector Addition

Vectors and Scalars Vector Addition

Scalar A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a

Scalar A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it. Magnitude – A numerical value with units. Scalar Example Magnitude Speed 20 m/s Distance 10 m Age 15 years

Vector Velocity Magnitude & Direction 20 m/s, N Acceleration 10 m/s/s, E A VECTOR

Vector Velocity Magnitude & Direction 20 m/s, N Acceleration 10 m/s/s, E A VECTOR is ANY quantity in physics Force 5 N rght that has BOTH MAGNITUDE and DIRECTION. Displacement +20 m

Applications of Vectors Example #1: A man walks 50 m east, then another 30

Applications of Vectors Example #1: A man walks 50 m east, then another 30 m east. Calculate his displacement relative to where he started? REPRESENTING VECTORS – ARROW tail head VECTOR ADDITION – Use the head to tail method Make a Vector Diagram (a picture that shows the given vectors in aproblem) and solve using Equations. 1) draw one vector 2) connect the tail of the 2 nd vector to the head of 1 st vector 3) Draw a 3 rd vector (resultant – final vector) from the tail of the 1 st vector to head of the 2 nd vector ∆d 1 = 50 m, E ∆d 2 = 30 m, E ∆dt = ∆d 1 + ∆d 2 = (+50 m) + (+30 m) ∆dt = +80 m or 80 m E Notice that the SIZE of the arrow conveys MAGNITUDE and the way it was drawn conveys DIRECTION.

Applications of Vectors • Example #2: A man walks 50 m east, then 30

Applications of Vectors • Example #2: A man walks 50 m east, then 30 m west. Calculate his displacement relative to where he started? 50 m, E 20, E 30 m, W ∆dt = ∆d 1 + ∆d 2 = (+50 m) + (-30 m) = +20 m or 20 m E

Perpendicular Vectors When 2 vectors are perpendicular, you must use the Pythagorean theorem. Example

Perpendicular Vectors When 2 vectors are perpendicular, you must use the Pythagorean theorem. Example #3: A man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT. T. N A LT U S E ∆d t =R Horizontal Component Finish ∆dy = 55 km, N Vertical Component ∆dx = 95 km, E Start The LEGS of the triangle are called the COMPONENTS

BUT……what about the direction? In the previous example, DISPLACEMENT was asked for and since

BUT……what about the direction? In the previous example, DISPLACEMENT was asked for and since it is a VECTOR we should include a DIRECTION on our final answer. ∆dy = 55 km, N N W of N ∆dx = 95 km, E E of N N of E N of W E W S of E W of S E of S S So the COMPLETE final answer is : 109. 8 km, 30 degrees North of East

Example #4: A person walks 10 m east, then walks 5 m north, then

Example #4: A person walks 10 m east, then walks 5 m north, then walks 20 m east. What is the total displacement? Steps: 1. Make a vector diagram as in the previous problems. 2. We nee to know the total displacement in the x-direction and the y-direction to use trig. 1. Add the two x-vectors together to make one new vector. 2. Make a new RT triangle and use trig. Final Answer = 30. 4 m 9. 5 o N of E