Physics Help Please!!!!!!!!??????????
A light plane is headed due south with a speed of 200 km/h relative to still air. After 1.00 hour, the pilot notices that they have covered only 125 km and their direction is not south but 15.0∘ east of south.
Part A
What is the wind velocity (magnitude)?
Part B
What is the wind velocity (direction)?
Can you please explain the steps. I tried it with triangle but kept getting the wrong answer.
Thanks in advance.
回答 (2)
These problems can be very confusing.
Velocity of plane relative to ground = vpg
Velocity of plane relative to air = vpa
Velocity of air relative to ground = vag
vpg =vpa + vag (note the pattern of letters)
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When drawing triangle ABC let:
vpa = AB
vag = BC
then that means vectorAB + vectorBC = vectorAC. So we can say
vpg = AC
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vpa = 200km/h south
With a scale of 1mm representing 1km/h, vpa is line AB, 200mm long pointing south.
A
.
.
B
vpg = 125km/h 15.0∘ east of south.
Represent vpg as line AC, 125mm long pointing 15.0° east of south(hour-hand at 6:30 on a 12-hour clock face).
A
. C
The complete triangle is therefore is like this:
A
. C
B
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We want vag (BC). Using the cosine rule:
BC² = AC² + AB² - 2.AC.AB.cos(∠A)
. . . .= 125² + 200² = 2x125x200cos(15°)
. . . .= 7329
BC = 85.6km/h.
This is the answer to part A. You might be expected to round to 86km/h.
______________________________
Using the sine rule:
AC/sinB = BC/sinA
125/sin B = 85.6/sin(15°)
sinB = 0.378
B = sin⁻¹ (0.378) = 22° approx,
So (referring to the direction of BC on the triangle-diagram above) we see the wind direction is 22° east of north.
收錄日期: 2021-04-18 00:10:02
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