Optimizing River Crossing Time for a Hunter Using a Powerboat

[joe215]

1. Homework Statement

A hunter wishes to cross a river that is 1.5 km wide and flows with a speed of 5.0km/h parallel to its banks. the hunter uses a small powerboat that moves at a maximum speed of 12 km/h with respect to the water. What is the minimum time necessary for crossing?


3. The Attempt at a Solution

5km/h^2 + 12Km/h^2=sq rt 169km/h^2 = 13 km/h

The hunter moves really moves at 13 km/h to the right because of the water moving upstream. 13 is the vector resultant of 5 north and 12 east.

So, T=D/V

T=width of stream/velocity of hunter
T=1.5km/12km/h = 0.125 h

 

[lisab]

1. Homework Statement

A hunter wishes to cross a river that is 1.5 km wide and flows with a speed of 5.0km/h parallel to its banks. the hunter uses a small powerboat that moves at a maximum speed of 12 km/h with respect to the water. What is the minimum time necessary for crossing?


3. The Attempt at a Solution

5km/h^2 + 12Km/h^2=sq rt 169km/h^2 = 13 km/h

The hunter moves really moves at 13 km/h to the right because of the water moving upstream. 13 is the vector resultant of 5 north and 12 east.

So, T=D/V

T=width of stream/velocity of hunter
T=1.5km/12km/h = 0.125 h

You calculate the correct velocity of the hunter (V = 13 km/h), but when you calculated his time of crossing you used V = 12 km/h.

 

[joe215]

If I used 13km/h instead of 12km/h, would the answer be right?