A research vessel is moving in a straight line at a constant speed of 10ms−1 relative to the water. At an instant when its sonar transducer is exactly below the bridge, the vessel emits an ultrasonic pulse toward a stationary whale directly ahead on the ship’s path. The reflected signal is received 8.4s after emission. The speed of sound in sea water under the prevailing conditions is 1450ms−1.
(a) Derive an expression relating the initial distance d between the vessel and the whale to the vessel speed u, the sound speed v, and the measured round-trip time t.
(b) Using the given data, determine the initial distance d when the pulse was emitted.
(c) Calculate the separation between the vessel and the whale at the instant the echo is received.