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

[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

The correct answer is: 0.9min. Please help!

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

 

[HallsofIvy]

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.

 

[Morphayne]

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...