Two ships are moving along a line due east. The trailing ship has a speed relative to land based observation point of `64.0(km)/(h)`, and the leading ship has a speed of `45.0(km)/(h)` relative to that point. The two ships are in a region of the ocean where the current is moving uniformly due west at `10.0(km)/(h)`. The trailing ship transmits a sonar signal at a frequency of 1200.0 Hz. What frequency is monitored by the leading ship? Use `1520(m)/(s)` as the speed of sound in ocean water.

Explanation

To solve the problem of finding the frequency monitored by the leading ship, we will use the Doppler effect formula for sound waves. Here are the steps to arrive at the solution:

### Step 1: Determine the effective speeds of the ships
- The trailing ship has a speed of 64.0 km/h relative to the land. The current is moving at 10.0 km/h due west, which means we need to add the speed of the current to the trailing ship's speed because both are moving in the same direction (east).
\[ V_T = 64.0 \, \text{km/h} + 10.0 \, \text{km/h} = 74.0 \, \text{km/h} \]
- The leading ship has a speed of 45.0 km/h relative to the land. Similarly, we add the speed of the current.
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