The canoeist crossing a river

[r.meghdies]

A canoeist who can paddle 5km/h in still water wishes to cross a 400 m wide river, with 2km/h current. If he steers the canoe perpendicular to the current and wants to get straight across the river how long will it take him to cross the river.

Which way is right? and why?

hypotenuse = 5 km/h
...| (ignore dots)
...| < 2 km/h
__________|
^ 400 m & 4.58 km/h
Θ = 22*

option 1:

t = 0.4 km / 4.58 km/hoption 2:
cosΘ = a / h
cos 22 = 0.4 km / h
h = 0.43 km

now i do t= .43km / 4.58 km/h

t= 5.63 minutes

 

[anathema]

I would say that option 2 is the correct way to solve this problem. This is because it takes into account the vector components of the canoe's motion in both the horizontal and vertical directions. By using trigonometry, we can find the hypotenuse of the triangle formed by the canoe's velocity in still water (5 km/h) and the current (2 km/h). This hypotenuse, or the resultant velocity, is the actual speed at which the canoe will be moving across the river.

Option 1 only considers the distance and the resultant velocity, but it does not take into account the direction of the canoe's motion. This can lead to an incorrect answer because the canoe will not be moving directly across the river, but at an angle due to the current. By using the trigonometric formula and finding the horizontal component of the resultant velocity, we can accurately calculate the time it will take for the canoe to cross the river.

Therefore, option 2 is the correct way to solve this problem because it considers both the distance and the direction of the canoe's motion. It is important for scientists to use accurate and precise methods when solving problems, and in this case, option 2 provides a more accurate solution.

 

[Moetasim]

I would approach this problem using the principles of physics and mathematics. The first step would be to draw a diagram to visualize the situation. From the given information, we can see that the canoeist needs to cross a 400 m wide river with a 2 km/h current and can paddle at 5 km/h in still water.

As the canoeist steers the canoe perpendicular to the current, we can use the Pythagorean theorem to calculate the resulting velocity. The hypotenuse of the triangle represents the resulting velocity, which is the combination of the paddling speed and the current speed. Using the Pythagorean theorem, we can calculate the resulting velocity to be approximately 4.58 km/h.

Next, we need to determine the time it will take the canoeist to cross the river. We can use the formula d = vt, where d is the distance, v is the velocity and t is the time. In this case, the distance is 400 m and the velocity is 4.58 km/h. Converting the distance to kilometers, we get 0.4 km. Substituting these values into the formula, we get t = 0.4 km / 4.58 km/h = 0.087 hours or approximately 5.2 minutes.

Therefore, it will take the canoeist approximately 5.2 minutes to cross the river if they steer the canoe perpendicular to the current. This is the correct way to approach this problem as it takes into account the resulting velocity and the distance to be covered.