Question bank: Vectors: Decomposition

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Question 1:

Very Hard

An observer is located at point A in an open field and sees a plane flying in a straight line towards point C, which is 800 m away and forming an angle of 30 degrees with the ground. The plane, which is at an altitude of 400 m above the ground, is subject to a wind that causes it to move 20 m/s in the direction perpendicular to the line connecting points A and C, towards point B. Disregarding the effect of the wind, determine: 1) The horizontal component of the plane's velocity. 2) The vertical component of the plane's velocity. 3) The resultant velocity of the plane, considering the effect of the wind. Use sine and cosine of 30 degrees, where sin(30) = 0.5 and cos(30) = 0.87, and assume g = 10 m/s^2 for the acceleration due to gravity.

Vectors: Decomposition

Multidisciplinary Question

Question 2:

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 3:

Easy

If a vector P has parallel components Px and Py, then the resulting vector will have a direction equal to the vector sum of Px and Py.

Vectors: Decomposition

Question 4:

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

Question 5:

Medium

An airplane flies in a straight line at an angle of 30º with respect to the ground. If the airplane's speed is 500 km/h, what is the horizontal component of the velocity?

Vectors: Decomposition

IARA TIP

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