Relative velocity boat crossing a river

[Woolyabyss]

Homework Statement

A boat crosses river, 240 m wide,which flows parallel to the straight banks with velocity
v1 = 12i, while the velocity of the boat relative to the river is v2 = 5j where v1 and v2 are measure in m/s

(i) find the magnitude of the actual velocity of the boat.

(ii) find how long it takes the boat to cross the river and the distance it has traveled downstream in doing so

Homework Equations

The Attempt at a Solution

(i)(12^2 + 5^2)^(1/2) = 13 m/s

(ii) relative distance/relative speed = 240/5 =48 s

48(12) =576 m

can somebody tell if part (ii) is right the back of my book seems to use 12 as the relative speed since it says it takes 20 seconds.
Any help would be appreciated.

 

[ehild]

Your solution is correct.

ehild

 

[tiny-tim]

yes, it looks as if the book has got the 12 and the 5 the wrong way round

 

[Woolyabyss]

Thanks.

 

[Nickie]

I would approach this problem by first clarifying the given information and the assumptions made. It is assumed that the boat is moving in a straight line and the river is flowing parallel to the banks. Also, the velocities of the boat and the river are given as v1 = 12i and v2 = 5j, respectively. It is important to note that these velocities are in vector form, with i and j representing the x and y directions, respectively.

To find the magnitude of the actual velocity of the boat, we can use the Pythagorean theorem to calculate the resultant velocity. The resultant velocity (v) can be expressed as v = √(v1^2 + v2^2), where v1 and v2 are the x and y components of the velocity, respectively. Therefore, the magnitude of the actual velocity of the boat is √(12^2 + 5^2) = 13 m/s.

To find the time it takes for the boat to cross the river and the distance it travels downstream, 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 traveled is equal to the width of the river, which is 240 m. Therefore, we can write the equation as 240 m = v*t.

To find the time, we need to determine the relative speed of the boat and the river. The relative speed can be calculated by subtracting the velocity of the river (v2 = 5j) from the velocity of the boat (v1 = 12i). This gives us a relative speed of √(12^2 + (-5)^2) = √(144 + 25) = √169 = 13 m/s.

Substituting this value in the equation, we get 240 m = (13 m/s)*t. Solving for t, we get t = 240 m / 13 m/s = 18.46 s. Therefore, it takes the boat approximately 18.46 seconds to cross the river.

To find the distance traveled downstream, we can use the formula d = vt again. In this case, the velocity is the relative speed of 13 m/s and the time is 18.46 s. Substituting these values, we get d = (13 m/s)*(18.46