How to solve a word problem using vectors

The video tutorial explains how to find the actual ground speed and direction of an airplane considering wind impact. It involves graphing vectors, calculating their components using trigonometry, and understanding the resultant vector through vector addition. The tutorial emphasizes the importance of using correct angles and storing values to avoid errors. Finally, it demonstrates how to calculate the magnitude and direction of the resultant vector, providing a comprehensive understanding of the problem.

What is the initial speed of the airplane before considering the wind?

• 100 mph

• 75 mph

• 300 mph

• 50 mph

What is the correct angle to use for the airplane's vector when calculating its components?

• 100 degrees

• 10 degrees

• 90 degrees

• 50 degrees

How does the wind affect the airplane's ground speed?

• It changes the direction only

• It increases the speed

• It has no effect

• It decreases the speed

What method is used to find the resultant vector of the airplane and wind?

• Subtraction of vectors

• Addition of vectors

• Multiplication of vectors

• Division of vectors

Why is it important to store calculated values during vector addition?

• To save time

• To make calculations easier

• To avoid rounding errors

• To ensure accuracy

What is the magnitude of the resultant vector?

• 343.7 mph

• 300 mph

• 75 mph

• 400 mph

What is the bearing of the resultant vector?

• N 50 degrees E

• N 89 degrees E

• N 1 degree E

• N 10 degrees W

What trigonometric function is used to find the angle of the resultant vector?

• Sine

• Cosine

• Tangent

• Cotangent

What is the significance of the resultant vector in this problem?

• It represents the airplane's speed only

• It represents the wind's speed only

• It represents the combined effect of airplane and wind

• It represents the direction of the wind

What is the correct way to express the direction of the resultant vector?

• As a speed

• As a bearing

• As a distance

• As a standard angle