An aeroplane flies at an average speed of 950km/hr from town P(lat.40degreeS, long.29.5degreeW) due east to town Q and then due south to town R. If the distance from Q to R along their common longitude is 4,500km and the whole journey took 11 hours, calculate longitude of Q and latitude of R. NB: take radius of the earth =6,400km, pie =3.142

47867967697=876

If the change in longitude is θ radians, the WE distance is 6400θ km.

Since time = distance/speed, then (assuming a constant speed),

(6400θ + 4500)/950 = 11
θ = 0.9297 = 53.3°

So, now you know how far East Q is from P.

As for QR, 4500 = 6400θ
so, again, find θ and convert to degrees. It is that far South of Q and P.

To calculate the longitude of town Q and the latitude of town R, we can use the given information about the distance, time, and speed of the airplane, as well as the Earth's radius.

Step 1: Calculate the distance covered from town P to town Q:
The distance covered from P to Q is in the east direction and can be calculated using the formula:
Distance = Speed × Time

Given:
Speed = 950 km/hr
Time = 11 hours

Distance(PQ) = 950 km/hr × 11 hrs

Step 2: Calculate the latitude of town Q:
Since the airplane flies due east from town P to town Q, the latitude remains the same. Therefore, the latitude of town Q is the same as the latitude of town P, which is -40 degrees (as given).

Latitude(Q) = -40 degrees

Step 3: Calculate the longitude of town Q:
To calculate the longitude of town Q, we need to find the distance covered by the airplane from town Q to town R along their common longitude. Let's call this distance QR.

Given:
Distance(QR) = 4,500 km

Step 4: Calculate the longitude difference covered by the airplane from Q to R:
Using the Earth's radius and the distance QR, we can calculate the longitude difference covered by the airplane.

Longitude difference(QR) = Distance(QR) / Earth's radius

Note: The Earth's radius is given as 6,400 km.

Longitude difference(QR) = 4,500 km / 6,400 km

Step 5: Calculate the longitude of town R:
Since the airplane flies due south from town Q to town R, the longitude remains the same. Therefore, the longitude of town R is the same as the longitude of town Q, which is 29.5 degrees West (as given).

Longitude(R) = 29.5 degrees West

Step 6: Calculate the latitude of town R:
Since the airplane flies due south from town Q to town R, we need to calculate the latitude difference covered by the airplane. The latitude difference depends on the time taken to cover the distance QR and the average speed of the airplane.

Latitude difference(QR) = Speed / Time

Latitude difference(QR) = 950 km/hr / 11 hrs

Step 7: Calculate the latitude of town R:
To find the latitude of town R, we subtract the latitude difference from the latitude of town Q.

Latitude(R) = Latitude(Q) - Latitude difference(QR)

Latitude(R) = -40 degrees - (950 km/hr / 11 hrs)

Now, let's perform the calculations.

Distance(PQ) = 950 km/hr × 11 hrs

Distance(PQ) = 10,450 km

Longitude difference(QR) = 4,500 km / 6,400 km

Longitude difference(QR) = 0.703 km

Latitude(R) = -40 degrees - (950 km/hr / 11 hrs)

Now, plug in the values:

Latitude(R) = -40 degrees - (950 km/hr / 11 hrs)

I apologize, it seems there may be an error in the question. The latitude difference cannot be directly determined with the given information.

Please double-check the question or provide additional information if available.

To solve this problem, we need to break it down into smaller steps. Let's start by calculating the time it took to travel from town P to town Q.

Step 1: Calculate the distance traveled from P to Q
Since the plane is flying due east from P to Q, the latitude remains the same, so we only need to consider the longitude. The distance traveled along the longitude can be calculated using the given average speed and time:

Distance = Speed × Time

Given that the average speed is 950 km/hr and the time taken is unknown, let's represent the time as 't'.

Therefore, the distance from P to Q can be calculated as follows:
Distance from P to Q = Speed × Time
Distance from P to Q = 950 km/hr × t km/hr

Step 2: Calculate the time taken from P to Q
To find the time taken, we need to divide the distance from P to Q by the average speed:

t = Distance from P to Q / Average speed
t = 950 km/hr × t km / 950 km/hr

As we can see, the average speed of 950 km/hr cancels out, leaving us with:
t = t km

So, the time taken from P to Q is t hours.

Step 3: Calculate the latitude and longitude of Q
Given that the latitude and longitude of P are 40°S and 29.5°W respectively, and the plane has flown due east, the latitude of Q remains the same (40°S). However, the longitude changes.

To find the longitude of Q, we need to add the distance traveled from P to Q to the longitude of P:
Longitude of Q = Longitude of P + Distance from P to Q

Longitude of Q = 29.5°W + t km

Now that we have the longitude of Q, we can move on to calculating the latitude of R.

Step 4: Calculate the latitude of R
The plane flies due south from Q to R. Since this is a straight line along the common longitude, the latitude remains the same. Therefore, the latitude of R is the same as the latitude of Q, which is 40°S.

Step 5: Calculate the longitude of R
The total distance from Q to R along their common longitude is given as 4,500 km. Since we already know the longitude of Q, we can calculate the longitude of R:

Longitude of R = Longitude of Q - Distance from Q to R

Longitude of R = (29.5°W + t km) - 4,500 km

Now, we have the longitude and latitude of both Q and R in terms of t. We can proceed to the next step.

Step 6: Calculate the value of t
The total journey time is given as 11 hours. We know that the time taken for the P-to-Q leg is t hours. Therefore, the time taken for the Q-to-R leg is 11 hours minus t hours:

Time from Q to R = Total journey time - Time from P to Q
11 hours = t hours + (11 hours - t hours)

Simplifying the equation gives us:
11 hours = t hours + 11 hours - t hours
11 hours = 11 hours

This equation holds true for any value of t, so we cannot determine t based on this information alone.

In conclusion, we can determine the longitude of Q as (29.5°W + t km) and the latitude of R as 40°S. However, we cannot determine the exact latitude and longitude coordinates without additional information such as the value of t or the actual distance traveled from P to Q.