The question states:(adsbygoogle = window.adsbygoogle || []).push({});

Two towns A and B are located directly opposite each other on a river 8km wide which flows at a speed 4km/h. A person from town A wants to travel to a town C located 6km up-stream from and on the same side as B. The person travels in a boat with maximum speed 10km/h and wishes to reach C in the shortest possible time. Let x(t) be the distance travelled upstream and y(t) be the distance travelled across the river in t hours. The person heads out at angle theta.

a) Show that x(t)=10tcos(theta)-4t and y(t)=10tsin(theta)

b) What is the angle theta and how long would the trip take?

Relevant equations:

So far I have used v=d/t along with some vector diagrams.

My attempt:

I have proven a) already by using v=d/t. The net velocity for x was equal to 10cos(theta)-4 and I just rearranged for x. I did the same to find y.

I then found the angle theta by saying that sin(theta)=8/10, therefore theta=arcsin(4/5). Also, I found the theta in terms of arccos which was theta=arccos(3/5). I found these by using a distance triangle with adjacent=6, opposite=8 and hypotenuse=10.

I then equated x(t)=6 ==> 10tcos(theta)-4t=6

10tcos(arccos(3/5))-4t=6

10t(3/5)-4t=6

6t-4t=6

t=3

And equated y(t)=8 ==> 10tsin(theta)=8

10tsin(arcsin(4/5))=8

10t(4/5)=8

8t=8

t=1

This is where I'm having problems. Shouldn't the time value be equal? If anyone could please help me out I would greatly appreciate it.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Parametric equations motion problem

**Physics Forums | Science Articles, Homework Help, Discussion**