A pilot is flying a Cessna airplane at 180 mph (airspeed).He would like to fly in the direction N45W, but there is a 32 mph wind in the S60W direction.What direction should the pilot set his course for in order to fly along his desired track? What will his speed relative to the ground be?
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To determine the direction the pilot should set his course for and the speed relative to the ground, we need to consider the effect of the wind on the airplane's path.
1. Calculate the wind's component in the N-S direction:
- The wind is coming from S60W, which means it has a component of 60 mph in the S direction.
- To determine the component in the N-S direction, we need to subtract this value from zero. So, the wind component in the N-S direction is -60 mph.
2. Calculate the wind's component in the E-W direction:
- The wind is coming from S60W, which means it has a component of 32 mph in the W direction.
- To determine the component in the E-W direction, we need to subtract this value from zero. So, the wind component in the E-W direction is -32 mph.
3. Determine the resultant wind vector:
- To find the resultant wind vector, we need to add the components from steps 1 and 2.
- So, the resultant wind vector is -60 mph (N-S direction) and -32 mph (E-W direction).
4. Determine the direction the pilot should set his course for:
- To identify the direction the pilot should set his course, we need to subtract the wind vector from the desired track.
- The desired track is N45W, which means it has a component of 45 mph in the N direction and 45 mph in the W direction.
- Subtracting the wind vector from the desired track, we have:
- N direction: 45 mph - 60 mph = -15 mph (meaning the pilot should set his course 15 mph in the S direction)
- W direction: 45 mph - 32 mph = 13 mph (meaning the pilot should set his course 13 mph in the E direction)
- Therefore, the pilot should set his course for S15E.
5. Calculate the speed relative to the ground:
- The speed relative to the ground is the sum of the airplane's airspeed and the component of the wind perpendicular to the desired track.
- The airspeed is given as 180 mph.
- The component of the wind perpendicular to the desired track is the E-W component (13 mph in the E direction).
- To calculate the speed relative to the ground, add the airspeed and the component of the wind:
- 180 mph + 13 mph = 193 mph
- Therefore, the speed relative to the ground will be 193 mph.
In summary, the pilot should set his course for S15E in order to fly along his desired track, and his speed relative to the ground will be 193 mph.