Final answer:
The cruise ship will not come to a stop at the right spot. It will overshoot and travel a distance of approximately 9765.63 meters.
Step-by-step explanation:
In order to determine if the cruise ship will come to a stop at the right spot, we need to calculate the time it takes for the ship to stop. We can use the equation:
vf = vi + at
where:
vf = final velocity (0 m/s)
vi = initial velocity (12.5 m/s)
a = acceleration (-0.08 m/s²)
t = time taken to stop
Substituting the given values, we get:
0 = 12.5 + (-0.08)t
Simplifying the equation:
t = 12.5 / 0.08
t ≈ 156.25 seconds
Now, we can calculate the distance traveled by the ship during this time:
d = vit + 0.5at²
Substituting the given values, we get:
d = 12.5 × 156.25 + 0.5 × (-0.08) × (156.25)²
d ≈ 9765.63 meters
Since the docking station is approximately 1.0 km away (1000 meters), the ship will not come to a stop at the right spot. It will overshoot and travel a distance of approximately 9765.63 meters.