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AnnZ [28]
3 years ago
7

An airplane is flying through the air at a speed of 150 mph at a heading of 60 degrees. if the wind is blowing at 20 mph from th

e south-east, (a) what is its ground speed, and (b) how far and (c) in what direction from its starting point will the plane be located after flying for 30 minutes.
Physics
1 answer:
Crazy boy [7]3 years ago
4 0

Answer:

Explanation:

Given

speed of plane 150 mph

heading 60^{\circ}

wind is blowing at 20 mph from south-east

velocity of plane w.r.t. wind

v_{pw}=150(\cos 60\hat{i}+\sin 60\hat{j})

v_{w}=20(\cos 45\hat{i}-\sin 45\hat{j})

v_{p}=v_{pw}+v_{w}

v_{p}=(150\cos 60+20\cos 45)\hat{i}+(150\sin 60-20\sin 45 )\hat{j}

v_{p}=89.14\hat{i}+115.76\hat{j}

|v_{p}|=146.103 m/s

(b)after 30 minutes

Plane traveled in  x direction =89.14\times 0.5=44.57 miles

Plane in Y direction =115.76\times 0.5=57.88 miles

Total distance=\sqrt{x^2+y^2}=73.05 miles

direction tan\theta =\frac{115.76}{89.14}=1.298

\theta =52.38^{\circ} w.r.t east

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