(6) Ilorin is at \( 8 \cdot 5^{\circ} \mathrm{N}, 4 \cdot 6^{\circ} \mathrm{E} \) and Freetown is at \( 8.5^{\circ} \mathrm{N}, 13 \cdot 3^{\circ} \mathrm{W} \). Calculate: a their distance apart, measured along the parallel of latitude b their distance from the equator c their speed, in \( \mathrm{km} / \mathrm{h} \), due to the rotation of the Earth.

To calculate the distances and speed, we'll break down the tasks separately. ### a) Distance Apart Along the Parallel of Latitude First, we can find the distance apart along the parallel of latitude using the formula: \[ \text{Distance} = \text{Longitude Difference} \times \cos (\text{Latitude}) \times \text{Earth's Radius} \] The longitude difference between Ilorin and Freetown: - Ilorin Longitude: \( 4.6^{\circ} \text{E} \) - Freetown Longitude: \( 13.3^{\circ} \text{W} \) which is equivalent to \( -13.3^{\circ} \text{E} \). Therefore, the longitude difference is: \[ \text{Longitude Difference} = |4.6 - (-13.3)| = |4.6 + 13.3| = 17.9^{\circ} \] Now, using the Earth's radius \( R \approx 6371 \text{ km} \) and the latitude of \( 8.5^{\circ} \): \[ \text{Distance} = 17.9 \times \cos(8.5^{\circ}) \times 6371 \text{ km} \] Calculating: \[ \cos(8.5^{\circ}) \approx 0.9877 \quad \Rightarrow \quad \text{Distance} \approx 17.9 \times 0.9877 \times 6371 \approx 1111.2 \text{ km} \] ### b) Distance from the Equator The distance from the equator can be calculated directly from the latitude using: \[ \text{Distance} = \text{Latitude} \times \left(\frac{\pi}{180}\right) \times \text{Earth's Radius} \] For both cities: \[ \text{Distance for Ilorin} = 8.5^{\circ} \times \left(\frac{\pi}{180}\right) \times 6371 \approx 149.0 \text{ km} \] \[ \text{Distance for Freetown} = 8.5^{\circ} \times \left(\frac{\pi}{180}\right) \times 6371 \approx 149.0 \text{ km} \] ### c) Speed Due to the Rotation of Earth The speed of rotation at the equator is about 1670 km/h. To find the speed at these latitudes, we use the cosine of the latitude: \[ \text{Speed} = 1670 \times \cos (\text{Latitude}) \] Taking the average latitude of approximately \( 8.5^{\circ} \): \[ \text{Speed} \approx 1670 \times \cos(8.5^{\circ}) \approx 1670 \times 0.9877 \approx 1642.74 \text{ km/h} \] So, summarizing: - The distance apart along the parallel of latitude is approximately **1111.2 km**. - The distance from the equator for both cities is approximately **149.0 km**. - The speed due to the rotation of Earth at this latitude is approximately **1642.74 km/h**.