Taking the radius of the earth ,R = 6370km and π22\7 . (A) Calculate the shortest distance between two cities P (24°N ,29° ,48°w) and Q(24°N,30°,12°E) along the parallel of latitude (a) nm ( 3mks) (b) Km (2mks) (c) If it's 1200hrs at p what is the local time at Q ( 2mks) ( B)An airplane few dew south from point A ( 60°N ,45°E) to a point B. The distance covered by the plane is 800km . Determine the position of B ( 3mks)

Part A: Calculate the shortest distance between two cities P and Q along the parallel of latitude.
Given:
P ($24^\circ N, 29^\circ 48' W$)
Q ($24^\circ N, 30^\circ 12' E$)
Radius of Earth ($R$) = 6370 km
$\pi = \frac{22}{7}$

Step 1: Convert longitudes to decimal degrees.
Longitude of P ($\lambda_P$) = $29^\circ 48' W = 29^\circ + \frac{48}{60}^\circ W = 29^\circ + 0.8^\circ W = 29.8^\circ W$
Longitude of Q ($\lambda_Q$) = $30^\circ 12' E = 30^\circ + \frac{12}{60}^\circ E = 30^\circ + 0.2^\circ E = 30.2^\circ E$

Step 2: Calculate the difference in longitude ($\Delta\lambda$).
Since the longitudes are in different hemispheres (West and East), add their absolute values.

$$\Delta\lambda = 29.8^\circ + 30.2^\circ = 60^\circ$$

The latitude ($\phi$) for both cities is $24^\circ N$.

a) Distance in Nautical Miles (NM)

Step 1: Use the formula for distance along a parallel of latitude in Nautical Miles.

$$$$