Final answer:
The boat moves approximately 0.7168 miles downstream by the time it reaches the far shore.
Step-by-step explanation:
When a boat is crossing a river, its resultant velocity is the vector sum of its velocity relative to the water and the velocity of the current. In this case, the boat is moving at a velocity of 72 mi/h due north relative to the water, and the river is flowing due east at 12 km/h. To find the resultant velocity, we can use the Pythagorean theorem.
Vresultant2 = Vboat2 + Vcurrent2
Plugging in the given values, we have:
Vresultant2 = (72 mi/h)2 + (12 km/h)2
Simplifying, we get:
Vresultant = sqrt((72 mi/h)2 + (12 km/h)2)
Converting units, we have:
Vresultant = sqrt((72 mi/h)2 + (7.5 mi/h)2)
Vresultant = sqrt(5184 mi2/h2 + 56.25 mi2/h2)
Vresultant = sqrt(5239.25 mi2/h2)
Vresultant = 72.40 mi/h
So, the resultant velocity of the boat is 72.40 mi/h.
To calculate how far downstream the boat moves, we can use the formula:
Distance downstream = Vresultant * time
Since the boat is traversing a 720 m wide river, the time it takes to cross is:
Time = Distance / Speed
Time = 720 m / 72.40 mi/h
Time = 0.00991 h
Now we can calculate the distance downstream:
Distance downstream = 72.40 mi/h * 0.00991 h
Distance downstream = 0.7168 mi
Therefore, the boat moves approximately 0.7168 miles downstream by the time it reaches the far shore.