Answer
The tanker will strike the reef. The tanker's speed when it hits the reef will be 0.173 m/s. Since the speed of the tanker is less than 0.2 m/s, the hull will be able to withstand the impact.
Work Step by Step
We can find the magnitude of the acceleration when the engine is operating.
$F = ma$
$a = \frac{F}{m} = \frac{8.0\times 10^4~N}{3.6\times 10^7~kg}$
$a = 2.22\times 10^{-3}~m/s^2$
We can find the time for the tanker to decelerate to rest.
$t = \frac{0-1.5~m/s}{-2.22\times 10^{-3}~m/s^2}$
$t = 676~s$
We can find the distance required to decelerate to rest.
$x = (1.5~m/s)(676~s)-\frac{1}{2}(2.22\times 10^{-3}~m/s^2)(676~s)^2$
$x = 507~m$
Therefore, since the distance to the reef is only 500 meters, the tanker will strike the reef.
We can find the velocity of the tanker after it moves 500 meters.
$v^2 = v_0^2+2ax$
$v = \sqrt{v_0^2+2ax}$
$v = \sqrt{(1.5~m/s^2)^2 - (2)(2.22\times 10^{-3}~m/s^2)(500~m)}$
$v = 0.173~m/s$
The tanker's speed when it hits the reef will be 0.173 m/s. Since the speed of the tanker is less than 0.2 m/s, the hull will be able to withstand the impact.
