The air speed indicator of a plane that took off from Detroit reads 373 km/h and the compass indicates that it is heading due east to Boston. A steady wind is blowing due north at 42.3 km/h.

Calculate the speed of the plane with reference to the ground.

If the pilot wishes to fly directly to Boston (due east) what must the compass read? (0 = North, 90 = East, ...)

X = east = 373km/h.

a. Y = north = 42.3km/h.

tanA = Y/X = 42.3 / 373 = 0.1134.
A = 6.47deg.

V = X / cosA = 373 / cos6.47 = 375.4km/h.

b. -6.47deg = 6.47deg South of East.
Get a 2nd opinion on this one.

Well, looks like the plane is facing a bit of a breeze up there! Let's try to figure out the speed of the plane with reference to the ground.

To do that, we need to use some aviation voodoo called vector addition. First, let's break down the velocity of the plane into its components: the eastward component (since it's heading due east) and the northward component (thanks to that pesky wind).

The eastward component of the plane's velocity is simply its airspeed indicator reading, which is 373 km/h.

Now, for the northward component, we have the wind blowing at 42.3 km/h directly north. Since the plane isn't affected in its heading by the wind, we can add the wind's northward component to the plane's northward component. In other words, we're adding 42.3 km/h to 0 km/h (the plane's northward component) to get 42.3 km/h total northward velocity.

To find the speed of the plane with reference to the ground, we can use the Pythagorean theorem: a^2 + b^2 = c^2 (where a and b are the eastward and northward components, and c is the total velocity with reference to the ground).

So, c^2 = 373^2 + 42.3^2.

Solving for c, we get c = sqrt(139129 + 1786.29) ≈ 373.11 km/h.

Therefore, the speed of the plane with reference to the ground is roughly 373.11 km/h.

Now, if the pilot wants to fly directly to Boston (due east), where the wind is blowing directly north, the compass should read 90 degrees. But hey, don't forget to double-check that compass for any sneaky magnets! Safety first, always. Happy landing!

To calculate the speed of the plane with reference to the ground, we can use vector addition.

Step 1: Convert the airspeed and wind velocity into vector form.

- Airspeed: 373 km/h due east
- Wind velocity: 42.3 km/h due north

Step 2: Add the vectors.

To add the vectors, we need to break them down into their respective components (east-west and north-south).

- For the airspeed:
- East-west component: 373 km/h
- North-south component: 0 km/h

- For the wind velocity:
- East-west component: 0 km/h
- North-south component: 42.3 km/h

Step 3: Add the components.

- East-west component: 373 km/h + 0 km/h = 373 km/h
- North-south component: 0 km/h + 42.3 km/h = 42.3 km/h

Step 4: Calculate the resultant velocity.

To calculate the resultant velocity, use the Pythagorean theorem.

Resultant velocity = √(east-west component^2 + north-south component^2)

= √(373 km/h)^2 + (42.3 km/h)^2)

= √(139129 km^2/h^2 + 1790.29 km^2/h^2)

= √140919.29 km^2/h^2

≈ 375.4 km/h

Therefore, the speed of the plane with reference to the ground is approximately 375.4 km/h.

To determine what the compass must read for the pilot to fly directly to Boston (due east), we need to consider the wind direction and its effect on the plane's heading.

Since there is a northward wind, the pilot would need to adjust the compass reading to compensate for the wind drift. The angle between the plane's actual heading and its intended heading is known as the drift angle.

To find the drift angle, we can use trigonometry.

Step 1: Calculate the drift angle.

Drift angle = arctan(north-south velocity / east-west velocity)

= arctan(42.3 km/h / 373 km/h)

≈ 6.5 degrees

Step 2: Determine the compass reading.

To fly directly east to Boston, the pilot needs to compensate for the drift angle. Therefore, the compass reading should be the intended heading minus the drift angle.

Compass reading = 90 degrees - 6.5 degrees

≈ 83.5 degrees

Thus, the compass should read approximately 83.5 degrees for the pilot to fly directly east to Boston.

To calculate the speed of the plane with reference to the ground, we need to consider the effect of the wind on the plane's actual velocity.

1. First, we decompose the velocity of the plane and the wind into their north and east components:
- The air speed indicator of the plane (373 km/h) represents its velocity relative to the air mass it moves through.
- The compass direction indicates that the plane is heading due east, so its motion with respect to the ground is in the eastward direction.
- The northward wind velocity is given as 42.3 km/h.

2. Now, we can determine the eastward and northward components of the plane's velocity with respect to the ground:
- The eastward component of the plane's velocity is given by the air speed indicator, which is 373 km/h.
- The northward component of the plane's velocity is the wind velocity, which is 42.3 km/h.

3. Since the wind is blowing due north and the plane's velocity is directly eastward, the two velocities (plane's velocity and wind velocity) are perpendicular to each other. Therefore, we can use the Pythagorean theorem to find the magnitude of the plane's velocity with respect to the ground:
- Magnitude of the plane's velocity = √(eastward component^2 + northward component^2)
- Magnitude of the plane's velocity = √(373^2 + 42.3^2)

4. Calculating the magnitude of the plane's velocity:
- Magnitude of the plane's velocity = √(139129 + 1787.29)
- Magnitude of the plane's velocity ≈ √140916.29
- Magnitude of the plane's velocity ≈ 375.53 km/h (rounded to two decimal places)

Therefore, the speed of the plane with reference to the ground is approximately 375.53 km/h.

Now, to determine what the compass should read for the pilot to fly directly to Boston (due east), we need to consider that the compass indicates the plane's heading, not its actual direction of motion with respect to the ground.

Since there is a crosswind blowing from the north, the pilot will need to compensate for the wind drift. The pilot should aim slightly west of due east to counteract the wind pushing the plane towards the east.

The amount of compensation required will depend on various factors including the wind speed and the plane's aerodynamics. Additionally, changes in wind speed and direction during the flight may require further adjustments to stay on course.

Therefore, to fly directly to Boston (due east), the compass should read slightly west of 90° (east) to account for the wind drift and maintain a straight path towards the destination. The exact heading would depend on the specific conditions of the flight.