An airplane is heading due south at a speed of 700 km/h .
Part A
Part complete
If a wind begins blowing from the southwest at a speed of 110 km/h (average), calculate the velocity (magnitude) of the plane relative to the ground. [Hint: First draw a diagram.]
Express your answer to three significant figures and include the appropriate units.
v =
627 kmh
Previous Answers
 Correct
Part B
Part complete
Calculate the velocity (direction) of the plane relative to the ground.
Express your answer to three significant figures and include the appropriate units.
θ =
7.13 ∘
east of south
Previous Answers
 Correct
Part C
Calculate how far from its intended position will it be after 10 min if the pilot takes no corrective action.
Express your answer to three significant figures and include the appropriate units.
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Δr =


Let's solve Part C by calculating the distance the plane will be from its intended position after 10 minutes if no corrective action is taken.

### Given:
1. **Wind velocity** (from the southwest) = 110 km/h
2. **Airplane's speed** (due south) = 700 km/h
3. **Time** = 10 minutes = \(\frac{10}{60}\) hours = \(\frac{1}{6}\) hours

### Approach:
1. The wind blows from the southwest, which means it has a component towards the east and a component towards the north. Since the wind is coming from 45 degrees to the south and west directions, we can resolve the wind's velocity into two perpendicular components: 
   - \(v_{\text{wind east}} = 110 \times \cos(45^{\circ})\)
   - \(v_{\text{wind north}} = 110 \times \sin(45^{\circ})\)

2. The displacement caused by the wind in 10 minutes will be the distance the wind pushes the plane in that time:
   - \(\Delta x = v_{\text{wind east}} \times t\)
   - \(\Delta y = v_{\text{wind north}} \times t\)

3. Calculate the resultant displacement from the intended position:
   - \(\Delta r = \sqrt{(\Delta x)^2 + (\Delta y)^2}\)

### Calculation:

Let's calculate this step-by-step.The plane will be approximately **18.3 km** away from its intended position after 10 minutes if no corrective action is taken.

Would you like more details on the calculations, or do you have any other questions?

Here are 5 related questions you might find interesting:
1. How would the displacement change if the wind speed were doubled?
2. What if the wind came from the northwest instead of the southwest?
3. How would the airplane's heading need to change to counteract the wind?
4. How does the wind's angle affect the resulting displacement?
5. What would be the time to reach a specific displacement if the wind speed changed?

**Tip:** Remember to convert all time units consistently when solving physics problems!

An airplane is heading due south at a speed of 700 km/h. If a wind begins blowing from the southwest at a speed of 110 km/h (average), calculate the velocity (magnitude) of the plane relative to the ground. Express your answer to three significant figures and include the appropriate units. Calculate the velocity (direction) of the plane relative to the ground. Calculate how far from its intended position it will be after 10 min if the pilot takes no corrective action.

Learn how to calculate the velocity of an airplane relative to the ground and its displacement after 10 minutes of wind blowing from the southwest. This problem covers vector addition, trigonometry, and the Pythagorean theorem. Perfect for high school students in Grades 10-12.

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