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

Answer:

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  $\= v + \= w =- 2500 \ km$

Step-by-step 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

   $\= v + \= w = 3000 -5500$

    $\= v + \= w =- 2500 \ km$