Answer
(a) The distance to one side of the fjord is $668~m$
(b) The captain will hear the second echo 2.78 seconds after hearing the first echo.
Work Step by Step
(a) We can find the speed of sound at a temperature of $5.0^{\circ}C$:
$v = 331+0.6~T$
$v = 331+(0.6)(5.0^{\circ}C)$
$v = 334~m/s$
We can find the distance the sound travels in a time of 4.0 seconds:
$d = v~t = (334~m/s)(4.0~s) = 1336~m$
Since the echo traveled to the side of the fjord and back to the ship, the distance to one side of the fjord is $\frac{1336~m}{2}$ which is $668~m$
(b) We can find the distance to the other side of the fjord:
$d' = 1800~m - 668~m = 1132~m$
For the sound to reach the other side of the fjord and come back to the ship as an echo, the sound must travel a distance of $(2)(1132~m)$ which is $2264~m$. We can find the time for the sound to travel this distance:
$t = \frac{2264~m}{334~m/s} = 6.78~s$
The captain hears the first echo after 4.0 seconds. Therefore, the captain will hear the second echo 2.78 seconds after hearing the first echo.
