Question bank: Vectors: Addition

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Question 1:

Medium

A sailor needs to determine the direction and resulting intensity of the wind, blowing from east to west at a speed of 15 m/s, and of a current flowing south at a speed of 10 m/s. Considering that the wind and the current are represented by the vectors 'V' and 'C', where 'V' points west and 'C' points south, determine the resultant vector 'R' of the combined action of the wind and the current. Then, calculate the angle that the resultant vector forms with the north axis, considering that the angle is positive counterclockwise and measured in the Cartesian plane.

Vectors: Addition

Theorical Question

Contextualized Question

Question 2:

Medium

Consider two vectors, A and B, both of magnitude 5 N, inclined at an angle of 60°. Using the parallelogram rule, determine the resultant of the sum of these vectors and calculate the angle between the resultant and vector A. Then, graphically represent vectors A, B, and the resultant.

Vectors: Addition

Question 3:

Medium

Maria and João are playing tag, and they run in different directions. Maria runs 4 meters in the northeast direction, while João runs 3 meters in the southeast direction. Consider the directions as vectors and represent these positions on the Cartesian plane (use x as east, y as north, and originated at the common starting point). (a) What is the result of the sum of the vectors corresponding to the displacements of Maria and João? (b) How much does the sum vector represent in distance between Maria and João? (c) Determine the direction of the sum vector in relation to the starting point.

Vectors: Addition

Question 4:

Medium

A race car is moving in the Cartesian plane and makes two consecutive displacements. First, the car travels 10 meters in the positive direction of the x-axis. Then, it turns 90 degrees to the right and travels 20 meters in the positive direction of the y-axis. What is the resultant vector of the car's displacement after the two movements?

Vectors: Addition

Question 5:

Medium

A student goes on a bike ride, initially heading 6 km north, then turning right and traveling 4 km east. Use the parallelogram rule to add the two vectors representing the journey. a) Represent the two vectors and build the parallelogram, b) Determine the resultant vector and calculate the magnitude of this vector, c) Calculate the angle formed between the resultant vector and the x-axis.

Vectors: Addition

IARA TIP

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