Exploring Vector Addition with the Pythagorean Theorem

Mrs. LaBarbera's video tutorial covers adding vectors using the Pythagorean theorem and trigonometric functions. It explains the conditions for using the theorem, the relationship between triangle sides, and how to calculate vector magnitudes and directions. The video includes practical examples and compares graphical and mathematical methods for accuracy.

What is the primary condition for using the Pythagorean theorem in vector addition?

• The vectors should be parallel.

• The vectors must be of equal magnitude.

• The vectors need to be perpendicular to each other.

• Any two vectors can be used.

What does 'C' represent in the Pythagorean theorem equation?

• One of the legs of the triangle.

• The angle opposite the hypotenuse.

• The area of the triangle.

• The hypotenuse of the triangle.

Which trigonometric function represents the ratio of the opposite side to the hypotenuse?

• Sine

• Cosine

• Tangent

• Cotangent

How do you find the direction of a resultant vector using trigonometry?

• Using the sine function only.

• By dividing the magnitude of one vector by another.

• Applying trigonometric functions based on known sides.

• Multiplying the vectors' magnitudes.

What is the result of adding two perpendicular vectors of 5 km North and 10 km West using the Pythagorean theorem?

• 15 km

• 7.5 km

• 11 km

• 10 km

What trigonometric function is used to find the angle of a resultant vector when the opposite and adjacent sides are known?

• Sine

• Cosine

• Tangent

• Secant

In the example of the model airplane and wind, what was the magnitude of the resultant velocity?

• 1.266 m/s

• 1.65 m/s

• 0.7 m/s

• 1.5 m/s

What angle did the resultant velocity make with the north in the model airplane example?

• 65 degrees

• 53 degrees

• 27 degrees

• 32 degrees

How is the magnitude of the girl's resultant displacement calculated in the bicycle example?

• Applying the Pythagorean theorem.

• Using vector addition graphically.

• Summing the distances traveled in each direction.

• By measuring the displacement directly.

What was the angle measured in the bicycle example using trigonometry?

• 32 degrees

• 53 degrees

• 65 degrees

• 27 degrees