Vectors

Vectors Vector: A quantity with both a magnitude and a direction. Vector: A quantity with both a magnitude and a direction. Scalar: A quantity with only a magnitude. Scalar: A quantity with only a magnitude.

When driving a car, the speedometer only shows a quantity (miles per hour), it does not show which direction you are driving. When driving a car, the speedometer only shows a quantity (miles per hour), it does not show which direction you are driving. Speed is therefore a. Speed is therefore a. scalar

Vectors Velocity is a vector because it has both a magnitude (the speed) and a direction (N, S, E, W, etc.) Velocity is a vector because it has both a magnitude (the speed) and a direction (N, S, E, W, etc.) “I was traveling west at 45 miles per hour” “I was traveling west at 45 miles per hour” directionmagnitude

Vectors In physics, vectors are represented by arrows. In physics, vectors are represented by arrows. The direction of the arrow is the same as the direction of the vector. The direction of the arrow is the same as the direction of the vector. The length of the arrow is proportional to the magnitude of the vector. The length of the arrow is proportional to the magnitude of the vector.

Vectors 45 mph This vector represents a car traveling eastward at 45 miles per hour.

Vectors 45 mph Even if the quantity is the same, a different direction means the vector is different. Notice that the length of the arrow didn’t change.

Vectors 45 mph If the car were to increase its speed, the vector would increase as well. 65 mph The length of the vector should be proportional to the magnitude.

Examples VectorsScalars

Vector Addition 55 mph Often, two or more vectors can be applied to the same object. In this case, the two vectors get added together. Suppose you are traveling on a train going 55 mph and then you were to run toward the front of the train at 7 mph. 7 mph

Vector Addition 55 mph Suppose you are traveling on a train going 55 mph and then you were to run toward the front of the train at 7 mph. 7 mph This is called the Head-to-tail method. The total velocity is the sum of these two vectors. This sum is called the Resultant. 62 mph

Vector Addition 55 mph 7 mph This is called the Head-to-tail method. The total velocity is the sum of these two vectors. This sum is called the Resultant. 62 mph

Vector Addition Vector addition also works for vectors moving in opposite directions. Suppose you now turn around on the train and run back at 7 mph. 55 mph 7 mph If we line these vectors up head-to-tail we get a different resultant. 48 mph

Vector Addition 4 mph Vector addition also works for vectors at angles to one another. Suppose a boat is rowing across a lake at 4 miles per hour when a 3 mile per hour cross current begins pushing the boat at a right angle to the boat. 3 mph

Vector Addition 4 mph 3 mph You can’t get the resultant by simply adding the numbers together. To find the resultant, you would need to use trigonometry. This is a triangle. 5 mph

Vector Addition 4 mph 3 mph Since all vectors require a direction, we also have to determine the direction of this resultant. 5 mph Sin θ = opposite hypoteneus θ 3 5 = θ = 37 o The resultant is 5 mph at 37 north of east. o