Boy Swim River: Time & Angle Calc

[Sauk]

A boy is swimming a river with a width of 65m. He is swimming from one side to the other at a constant speed of 2.3 m/s, and the current, parallel to the bank is moving at 1.1 m/s. How long will it take him to cross the river, and what will the angles be between his final path and the river bank be?

 

[blochwave]

You really should show a little more work, but just to prompt you:

You have two perpendicular vectors. One has magnitude 1.1, the other has magnitude 2.3

The resultant vector will be the actual path he follows and the resultant vector magnitude will be the actual speed he travels along that actual path

So how do you
A)Draw this? You can draw two perpendicular vectors of course, what does the resultant look like relative to those two?
B)Find the magnitude of the resultant vector?
C)Find the angle between the resultant vector and, in this case, the vector running parallel to the river bank?

 

[Moetasim]

I would approach this scenario by first gathering all the necessary information and data. From the given information, we know that the river has a width of 65m and the boy is swimming across it at a constant speed of 2.3 m/s. We also know that the current is moving parallel to the bank at a speed of 1.1 m/s.

To determine the time it will take for the boy to cross the river, we can use the formula time = distance/speed. In this case, the distance is the width of the river, which is 65m, and the speed is the combined speed of the boy and the current, which is 2.3 m/s + 1.1 m/s = 3.4 m/s. Therefore, the time it will take the boy to cross the river is 65m/3.4 m/s = 19.12 seconds.

To determine the angles between the boy's final path and the river bank, we can use the trigonometric formula tanθ = opposite/adjacent. In this case, the opposite side is the width of the river, which is 65m, and the adjacent side is the distance the boy has swum, which can be calculated by multiplying his speed (2.3 m/s) by the time it takes him to cross the river (19.12 seconds). This gives us a distance of 44.06m. Therefore, tanθ = 65m/44.06m = 1.48. Solving for θ, we get an angle of approximately 56 degrees.

In conclusion, the boy will take 19.12 seconds to cross the river and the angle between his final path and the river bank will be approximately 56 degrees. It is important to note that these calculations assume the boy swims in a straight line and does not deviate from his path due to the current. In reality, the angle and time may vary depending on the conditions of the river and the boy's swimming ability.