Question

The vector ~v represents the displacement vector from Portland, Oregon to Houston, Texas. The vector w~ represents the displacement vector from Houston, Texas to Akron, Ohio. Use the vectors ~v and w~ to answer the following questions:

a. What is the displacement vector Of a plane which flies from Akron, Ohio to Houston, Texas?
b. In order to fly home from Portland to Akron I have a layover in Houston. Find a vector which describes my total displacement over the whole trip.
c. It is approximately 3000 km from Portland to Houston. It is approximately 5500 km from Anchorage, Alaska to Houston. A plane flies in a straight line from Houston to Anchorage and during the flight it passes directly over Portland. Find a vector which describes the displacement of the plane.

Answer 1

a

the displacement of the plane is
`- \= w`

b

The displacement of plane from Portland to Akron with layover at Houston is

`\= v + \= w`

c

the vector which defines this displacement is
`\= v + \= w =- 2500 \ km`

Explanation:

From the question we are the

The displacement from Portland, Oregon to Houston, Texas. is
`\= v`

The displacement from Houston, Texas to Akron, Ohio. is
`\= w`a

a

The motion of the plane in question a is in the opposite direction to vector
`\= w`

So the displacement of the plane is
`- \= w`

b

The motion of Portland to Houston to Akron is in the direction of both vector
`\= v` and
`\= w` so

The displacement of plane from Portland to Akron with layover at Houston is

`d = \= v + \= w`

c

From the question we are told that the plane flies over Portland to get to Anchorage, Alaska which implies that it is moving in opposite direction to the vector
`\= v`

Give that distance from Portland to Houston is
`\= v = 3000 km`

and the distance from Portland to Anchorage is
`\= w = - 5500`km

Then the vector which defines this displacement is mathematically represented as

`\= v + \= w = 3000 -5500`

`\= v + \= w =- 2500 \ km`