Cross a River: Time Needed for 1.5km Distance at 6.6km/h Speed

[megamax48]

Homework Statement

A hunter wishes to cross a river that is 1.5 km
wide and that flows with a speed of 6.6 km/h.
The hunter uses a small powerboat that moves
at a maximum speed of 14 km/h with respect
to the water.
What is the time necessary for crossing if
the boat goes directly across the river? An-
swer in units of min.

Homework Equations

?

The Attempt at a Solution

I don't even know where to start.

 

[drizzle]

welcome to PF megamax48

you need to find the net velocity acting on the boat, calculate the angle with respect to the boat speed vector [theta=tan[SUP]-1[/SUP] v_y/v_x=tan^-1 v_river/v_boat], get the distance using the angle and the river’s width, finally calculate the time using the calculated distance and the net velocity. you better draw this so you can understand it well

ps. don't forget to convert the units

 

[tomcue]

I would first gather all the necessary information and data in order to solve this problem. I would start by converting all the speeds to a common unit, such as meters per second. 6.6 km/h is equivalent to 1.83 m/s and 14 km/h is equivalent to 3.89 m/s.

Next, I would use the equation d = vt to calculate the distance the boat needs to travel across the river. In this case, the distance (d) is 1.5 km or 1500 meters and the velocity (v) is 3.89 m/s. Solving for time (t), we get t = d/v = 1500/3.89 = 385.8 seconds.

Since the answer is required in minutes, we can convert seconds to minutes by dividing by 60. So the time necessary for crossing the river is approximately 6.4 minutes.

It's important to note that this is a simplified calculation and does not take into account factors such as the direction and speed of the current, as well as any other potential obstacles in the river. I would also consider these factors and conduct further analysis to provide a more accurate and comprehensive answer.