A patrol ship tracks a submarine that is moving vertically upward through the water. Two successive sonar pulses are sent straight downwards from the ship at an interval of 2.0s. The first echo is received 1.50s after it is sent, and the second echo is received 1.48s after it is sent. Assume the speed of sound in sea water is 1500m/s throughout the region. Neglect any change in sound speed with depth.
(i) Let d1 be the distance of the submarine below the ship at the instant the first pulse is emitted. Express d1 in terms of the given quantities.
(ii) Obtain a similar expression for d2, the distance of the submarine below the ship when the second pulse is emitted.
(iii) Using your results, calculate the average vertical speed of the submarine between the two pulses. State clearly whether the submarine is rising or sinking.
(iv) Determine the depth of the submarine below the ship at the instant the second echo is received.