An airplane is flying toward the northwest Which of the foll

An airplane is flying toward the northwest. Which of the following wind velocity vectors increases the plane\'s speed the most? Which slows down the plane the most? Write a sentence explaing your reasoning.

The vectors are... w(1) = -4i-j , w(2) = i-2j , w(3)= -i+8j , w(4)= 10i+2j , w(5)= 5i-2j

The w(1,2,3,4,5) are all vectors.

Solution

Asuuming direction of place to be along -1i+1j and same speed for all winds,

the fastest would be for the one whose angle is least with the plane and the slowest would be because of the one which makes the largest angle.

a) -4i-j makes the least angle: 31 degrees. So it increases the speed the most.

b) 1i-2j makes the largest angles: 161.44 degrees. So it slows the plane down the most.

The angles can be found using the formula: v ^. w = ||v|| ||w|| cos(theta)