# Calculating Time for Rowing Across a River: A Vectors Word Problem

• Morphayne
In summary, Pierre is attempting to row across the river at a speed of 10 km/h and is being held back by the speed of the river. His speed made good across the river is 0.6 km/h.
Morphayne

## Homework Statement

I'm not sure if I posted this in the right section, I apologize If I did anything wrong.

I am stuck on part 15(b), so I just wrote my answer down for the parts I got right because I felt that it is relevant information. I posted question 14 because question 15 is just an extension. The correct answer for 15(b) is 0.9min.

Question 14:
In his rowboat, Pierre heads directly across a river at a speed of 10km/h. The river is flowing at 6km/h.
a) What is the resultant speed of the boat?
b) What angle will the resultant path of the boat make with the shoreline?
c) If the rover is 120m wide, how far downstream will Pierre land on the opposite shore?

Answer (a) = 11.7km/h
Answer (b) = 59 degrees
Answer (c) = 72m

Question 15:
Refer to exercise 14. Suppose Pierre want to row directly across the river.
(a)At what angle relative to the shoe should he head?
(b)How long will this trip take?

Answer (a) = 53.1 degrees
Answer (b) = This is where I need help.

## Homework Equations

velocity = distance/time

## The Attempt at a Solution

Attempt 1:
From question 14: Distance = 120m = 0.12km
From question 14(a): Velocity = 11.7km/h

So; Time = 0.12/11.7
= 0.01025641 hours *60
= 0.62 min.

Attempt 2:
Distance = 120m
Velocity = 11.7km/h = 3.3m/s

So; Time = 120/3.3
= 36.4s /60
= 0.61min

Last edited:
It should be obvious that the velocity from problem 14 is NOT the velocity he makes in problem 15! According to your calculations, he is heading at 53.1 degrees upstream and making speed 10 mph in that direction but is being set back by the speed of the river.

Calculate his "speed made good" across the river in the same way (I presume) you did in problem 14: Set up the velocity vector so you have a right triangle with angle 53.1 degrees and hypotenuse of length 10 km/h. His speed across the river is the "near side" of that right triangle so cos(53.1)= v/10.

But when I solve cos(53.1) = v/10 for v I get:

v = 10 cos(53.1)
v = 0.6km/h

Then:

Time = distance/velocity
Velocity = 0.6km/h
Distance = 120m = 0.12km

So; Time = 0.12/0.6
Time = 0.20 min

The correct answer is 0.9 min.

Maybe a picture will help. Sorry if I'm asking too much, I'm just so frustrated with math class right now...

## 1. What is the definition of a vector in physics?

A vector is a quantity that has both magnitude and direction. In physics, it is represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

## 2. How do you add vectors using the graphical method?

To add vectors using the graphical method, you must first draw each vector on a graph with the appropriate scale. Then, place the tail of the second vector at the head of the first vector. The resultant vector is the vector from the tail of the first vector to the head of the second vector.

## 3. How do you add vectors using the component method?

The component method involves breaking down each vector into its x and y components. Then, add the x components and the y components separately to find the resultant vector. The magnitude and direction of the resultant vector can then be determined using trigonometry.

## 4. What is the difference between adding vectors algebraically and graphically?

Adding vectors algebraically involves using the Pythagorean theorem and trigonometry to find the magnitude and direction of the resultant vector. Graphically adding vectors involves drawing the vectors on a graph and finding the resultant vector using the graphical method.

## 5. How do you handle negative vectors when adding them?

When adding negative vectors, you must take into account their direction. If the negative vector is in the opposite direction of the positive vector, then you would subtract the magnitude of the negative vector from the magnitude of the positive vector. If the negative vector is in the same direction as the positive vector, then you would add the magnitudes of both vectors.

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