1.(arrow above letter a pointing to the right) and (arrow above letter b pointing to the right) have the same direction, and they both have a magnitude of 6. What must be true about(arrow above letter a pointing to the right)and(arrow above letter b pointing to the right)?
They are equal and parallel.
~ They are opposites, but not parallel.
They are opposites and parallel.
They are equal, but not parallel.
2.A plane is flying due east with a velocity of 90 m/s. The wind is blowing out of the north at 4 m/s. What is the magnitude of the plane’s resultant velocity? Round your answer to the nearest tenth.
86.0 m/s
~89.9 m/s
90.1 m/s
109.9 m/s
I think these are right but then again i could be completely wrong. Please check.
why not just specify that a and b are vectors?
Then the problem is:
vectors a and b point in the same direction, and have magnitude 6.
answer: equal and parallel.
sqrt(90^2+4^2) = 90.088 ~ 90.1
For question 1, the arrows above letter a and letter b represent vectors. In order to determine the relationship between these vectors, we need to consider both their direction and magnitude.
If the two vectors have the same direction (pointing to the right) and the same magnitude (6), then they are equal vectors. Additionally, since they have the same direction, they are also parallel to each other. Therefore, the correct answer is: They are equal and parallel.
For question 2, we need to find the resultant velocity of the plane considering both its velocity and the wind velocity. Since the plane is flying due east with a velocity of 90 m/s and the wind is blowing out of the north at 4 m/s, we can use vector addition to find the resultant velocity.
Using the Pythagorean theorem, we can combine the eastward and northward components of the velocities. The eastward component with magnitude 90 m/s is unaffected by the wind, while the northward component with magnitude 4 m/s is perpendicular to it.
By forming a right-angled triangle, we can calculate the magnitude of the resultant velocity using the formula:
Resultant velocity = sqrt((90^2) + (4^2))
Calculating this would give us approximately 90.1 m/s. Rounding to the nearest tenth, the correct answer is: 90.1 m/s.
Therefore, your answer for question 1 is correct, and for question 2, the correct answer is: 90.1 m/s.