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jhhong1247 jhhong1247
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10 years ago
You are traveling on an airplane. The velocity of the plane with respect to the air is 190 m/s due east. The velocity of the air with respect to the ground is 32 m/s at an angle of 30° west of due north.

What is the heading of the plane with respect to the ground? (Let 0° represent due north, 90° represents due east).

How far east will the plane travel in 1 hour?


Please help me with this question !! I have tried to solve it for more than two hours ; Smiling Face with Open Mouth and Cold Sweat ;(
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wrote...
10 years ago
Okay, I finished answering this with 170 as the velocity and a velocity of the air with respect to the ground of 32 m/s. You may use the same strategy.. Slight Smile

The velocity of the plane with respect to the air v = 170 i m/s
The velocity of the air with respect to the ground v ' = 32 cos 30 x (-i) + 32 sin 30 x ( j )

= -27.712 i + 16 j

1)The velocity of the plane with respect to the ground v " = v - v '

=197.712 i -16 j

The speed of the plane with respect to the ground v " = SQRT[ 197.712 2 + (-16) 2 ]

= 198.358 m / s

2)The heading of the plane with respect to the ground θ = tan - 1( 16 / 197.712 )

= 4.626 degrees south of east

3)Time t = 1 h

= 3600 s

Distance travel by plane in east direction with in 1 hour time = Speed in east x time

= 197.712 m / s x 3600 s

= 711.763 km
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