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Answer:
The actual speed = 27.12 mi/h
Direction = 36.5° in NE(north of east)
Step-by-step explanation:
As given , A hot air balloon is flying at a constant speed of 20 mi/h at a bearing of N 36° E.
⇒θ = 36°
Let v₀ be the constant speed, then v₀ = 20
Let vₓ be the speed in East direction
be the speed in North direction
So,
vₓ = v₀ sin(θ) = 20 sin(36°) + 10 ( As given, There is a 10mi/h cross wind blowing due east.)
⇒vₓ = 20(0.588) + 10 = 11.76 + 10 = 21.76 mi/h
and = v₀ cos(θ) = 20 cos(36°) = 20(0.809) = 16.18 mi/h
Now,
the actual speed = √(vₓ)² + ()²
= √(21.76)² + (16.18)²
= √473.498 + 261.792
= √735.29 = 27.12
⇒The actual speed = 27.12 mi/h
Now,
Direction = θ =
⇒ Direction = 36.5° in NE(north of east)