Two airplanes taxi as they approach the terminal. Plane 1 taxies with a speed of
ID: 1407403 • Letter: T
Question
Two airplanes taxi as they approach the terminal. Plane 1 taxies with a speed of 11.6 m/s due north. Plane 2 taxies with a speed of 7.18 m/s in a direction 23.4° north of west. What is the direction of plane 1 relative to plane 2? Give the angle counterclockwise relative to the north.
b. What is the magnitude of the velocity of plane 1 relative to plane 2?
c. What is the direction of plane 2 relative to plane 1? Give the angle counterclockwise relative to the north.
d. What is the magnitude of the velocity of plane 2 relative to plane 1?
Please help. Homework due soon and Ive tried numerous times. I cant figure it out. Please help thank you!
Explanation / Answer
here,
speed of plane 1 taxies, v1 = 11.6 j m/s
speed of taxies 2 , v2 = 7.18 (- cos(23.4) + sin(23.4))
v2 = ( - 6.59 i + 2.85 j ) m/s
v1 - v2 = 6.59 i + 8.75 j m/s
(a)
the direction of plane 1 relative to plane 2 , theta = arctan(8.75/6.59)
theta = 53.01 degree
the direction of plane 1 relative to plane 2 is 323.01 degree counterclockwise from north
(b)
|v1-v2| = sqrt(6.59^2 + 8.75^2)
|v1 - v2| = 10.9 m/s
the magnitude of the velocity of plane 1 relative to plane 2 is 10.09 m/s
(c)
v2 - v1 = - 6.59 i - 8.75 j m/s
the direction of plane 1 relative to plane 2 , theta = arctan(8.75/6.59)
theta = 53.01 degree
the direction of plane 2 relative to plane 1 is 143.01 degree counterclockwise from north
(d)
|v2 -v1| = sqrt(6.59^2 + 8.75^2)
|v2 - v1| = 10.9 m/s
the magnitude of the velocity of plane 2 relative to plane 1 is 10.09 m/s