# Vector Math Problem (Boat crossing a River)

• zetlearn
In summary, the problem statement asks for an angle of 50 degrees relative to the current direction. They give you a start time and the velocities, so it seems like they want you to verify that the boat makes it straight across. So why are you trying to calculate an angle?
zetlearn
Homework Statement
(a) At what angle Sumon has to drive the boat to reach college at time?

Context: The 4 km width river is situated in front of Sumon's house and his college is in opposite of that river. One day Sumon started his journey for college at 7.30 am by making an angle of 50° with a velocity of 5 km/h. College starts at 8.30. Velocity of current is 2 km/h.
Relevant Equations
The 4 km width river is situated in front of Sumon's house and his college is in opposite of that river. One day Sumon started his journey for college at 7.30 am by making an angle of 50° with a velocity of 5 km/h. College starts at 8.30. Velocity of current is 2 km/h.
Is that correct?

Welcome to PF.

Please describe how you calculated that answer, and show all of your work that led to it. Thanks.

Oh, and 130 degrees with respect to what?

nasu and zetlearn
berkeman said:
Welcome to PF.

Please describe how you calculated that answer, and show all of your work that led to it. Thanks.

Oh, and 130 degrees with respect to what?
Respect to Direction of Current

Any idea how to solve it please??

Sorry, several things don't make sense. The problem statement seems to be giving you an angle of travel (with respect to a line that goes straight across the river, not pointing in the direction of the current). They give you a start time and the velocities, so it seems like they want to know when the boat reaches the other side (and probably want you to verify that the boat makes it straight across). So why are you trying to calculate an angle? Aren't you supposed to calculate the travel time?

berkeman said:
Sorry, several things don't make sense. The problem statement seems to be giving you an angle of travel (with respect to a line that goes straight across the river, not pointing in the direction of the current). They give you a start time and the velocities, so it seems like they want to know when the boat reaches the other side (and probably want you to verify that the boat makes it straight across). So why are you trying to calculate an angle? Aren't you supposed to calculate the travel time?
The question is: (a) At what angle Sumon has to drive the boat to reach college at time?

Then whay do you say that it travels at 50 degrees?
The text says: "by making an angle of 50°" .
You need a good, coherent question before even thinking of what the answer may be.

zetlearn said:
The question is: (a) At what angle Sumon has to drive the boat to reach college at time?
You seem to have interpreted the question as:

"At what angle (relative to directly downstream) must Sumon drive so that he covers exactly four miles (not necessarily in the right direction) in one hour of travel time?"

You correctly calculate that after one hour, the river will have carried Sumon 2 miles downstream. The boat will have travelled 5 miles relative to the water. We want the vector sum of that 2 mile vector and the 5 mile vector to have a magnitude of 4 miles. So you use the law of cosines and solve for the angle between the 2 mile vector (directly downstream) and the 5 mile vector (the direction taken by the boat).

Let us take this to the next step. Where will Sumon be after one hour if he follows your 130 degree heading?

Let us do it by components. We will use the ##x## axis for the direction of the current flow and the ##y## axis for the direction across the river toward the college. We will use ##w## for the distance travelled by the water and ##b## for the distance travelled by the boat relative to the water. We will use ##s## for the total distance.

##w_x = 2##, ##w_y = 0##
##b_x = 5 \cos 130 = -3.2##, ##b_y = 5 \sin 130 = 3.8##
##s_x = -1.2##, ##s_y = 3.8##

So he has made it only 3.8 miles across the river and has ended up 1.2 miles upstream.

Maybe he needs to aim more nearly directly across so that he actually hits the college instead of missing? Is it really a problem if he arrives early?

Last edited:

## 1. What is a vector math problem?

A vector math problem involves using mathematical concepts to solve problems related to vectors, which are quantities that have both magnitude and direction. In this specific problem, we are using vector math to calculate the speed and direction of a boat crossing a river.

## 2. How do you represent a vector in a math problem?

In a math problem, a vector is typically represented by an arrow pointing in a specific direction. The length of the arrow represents the magnitude of the vector, while the direction it points in represents the direction of the vector. In some cases, vectors may also be represented by coordinates or equations.

## 3. What is the difference between a scalar and a vector?

A scalar is a quantity that only has magnitude, while a vector has both magnitude and direction. For example, speed is a scalar quantity because it only tells us how fast something is moving, while velocity is a vector quantity because it tells us both how fast and in what direction something is moving.

## 4. How do you solve a vector math problem involving a boat crossing a river?

To solve a vector math problem involving a boat crossing a river, we first need to break down the problem into its components. This involves finding the horizontal and vertical components of the boat's velocity and the river's velocity. Then, we can use vector addition to find the resultant velocity of the boat, which will give us the speed and direction of the boat's movement.

## 5. What are some real-life applications of vector math?

Vector math is used in many different fields, including physics, engineering, and navigation. Some real-life applications include calculating the trajectory of a projectile, determining the forces acting on an object, and navigating a ship or airplane using wind speed and direction. It is also used in computer graphics to create 3D animations and video games.

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