Question bank: Vectors: Decomposition

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Question 1:

Medium

An airplane moves at a constant speed of 400 km/h relative to the ground, forming a 30º angle with the positive east-west axis (east direction) and the positive north-south axis (north direction). Considering two perpendicular vectors representing the airplane's trajectory, one parallel to the east-west axis and the other parallel to the north-south axis, answer: (a) What is the component of the velocity vector in the east-west axis? (b) What is the component of the velocity vector in the north-south axis? (c) Graphically represent the velocity vector and its components on the east-west and north-south axes.

Vectors: Decomposition

Question 2:

Medium

An airplane must travel from airport A to airport B. The route has a direction vector of 500 km in the Northeast direction. The pilot needs to find the components of the vector in the North and East directions to determine the flight path. a) Decompose the vector into its North and East components. b) If the airplane flies at a constant speed of 400 km/h, how long will it take to travel each component of the route? c) Determine the average velocity of the airplane considering both segments of the flight.

Vectors: Decomposition

Question 3:

Medium

An airplane is flying at a constant speed of 150 km/h in a direction 30º north of east. Considering that the perpendicular coordinates are the east-west (x) and north-south (y) directions, answer: (a) What is the component of the airplane's velocity in the east direction? (b) What is the component of the airplane's velocity in the north direction? (c) Sketch a vector diagram representing the described situation, showing the airplane's velocity, as well as the vector components you have just calculated.

Vectors: Decomposition

Question 4:

Medium

If a vector has direction upwards and leftwards, which of the following options would represent a vector that has two orthogonal components?

Vectors: Decomposition

Question 5:

Very Easy

An airplane takes off from an airport and starts its trajectory ascending at 30° in relation to the ground. If the airplane's velocity can be decomposed into two components, one parallel to the ground and another perpendicular to it, determine the component of the airplane's velocity that acts parallel to the ground, considering that the total velocity of the airplane is 200 m/s.

Vectors: Decomposition

Contextualized Question

Calculus Question

IARA TIP

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