Calculating Velocities and Times in a River Current: Solving for t in terms of c

[alexsphysics]

Homework Statement

While a boat cruises down a river it crosses a wooden log at a particular point in time. Then the boat travels along the river for time c and reverses its direction to travel upstream for a time t, when it meets the same wooden log, which has been freely drifting along all the while. If the engine of the boat has been working at the same power level throughout its journey then express t in terms of c.

Relevant Equations

I'm really not sure as to how I should be interpreting expressing t in terms of c. Any help would be appreciated, thanks!

I'm really not sure as to how I should be interpreting expressing t in terms of c. Any help would be appreciated, thanks

 

[fresh_42]

You have to show us your efforts. No idea is no reason. Have you drawn a picture? What do you know about velocity? Which variables do we have? There is a lot to start with.

 

[alexsphysics]

You have to show us your efforts. No idea is no reason. Have you drawn a picture? What do you know about velocity? Which variables do we have? There is a lot to start with.

I know that velocity is the change in the position of an object divided by the time, and the variables are t and c and it's asking to express t in terms of c, but what place does velocity have in this problem?

 

[fresh_42]

You have a river with a velocity, a boat with velocity, and three points on this river: the log for the first time, the turning point, and the log for the second time. This gives you a couple of equations. The formula for the distance $x$ traveled at a constant speed $v$ is $x(s)=v\cdot s + x_0$ where I used $s$ for the time on a clock, because you already used $t$ for something else, a certain duration. $x_0$ is the starting distance from the origin, depending on when you start the clock. I would set $x_0=0$ as the first encounter of the log.

 

[alexsphysics]

You have a river with a velocity, a boat with velocity, and three points on this river: the log for the first time, the turning point, and the log for the second time. This gives you a couple of equations. The formula for the distance $x$ traveled at a constant speed $v$ is $x(s)=v\cdot s + x_0$ where I used $s$ for the time on a clock, because you already used $t$ for something else, a certain duration. $x_0$ is the starting distance from the origin, depending on when you start the clock. I would set $x_0=0$ as the first encounter of the log.

I really am confused as to how I should continue from there

 

[fresh_42]

What are the velocities? Say the river floats at a speed of $v_r$ and the boat drives at $v_b$. Then we have $v_b+v_r$ as the speed along the river and $-v_b+v_r$ against the current. You also know the times necessary for the distances: $c$ along the current, $t$ upstream. The log travels at the speed of $v_r$, and its distance is $L(c+t) = v_r\cdot (c+t)$. You get similar equations for the boat. When they meet for the second time, $L(c+t)$ equals the position of the boat.

 

[alexsphysics]

What are the velocities? Say the river floats at a speed of $v_r$ and the boat drives at $v_b$. Then we have $v_b+v_r$ as the speed along the river and $-v_b+v_r$ against the current. You also know the times necessary for the distances: $c$ along the current, $t$ upstream. The log travels at the speed of $v_r$, and its distance is $L(c+t) = v_r\cdot (c+t)$. You get similar equations for the boat. When they meet for the second time, $L(c+t)$ equals the position of the boat.

Thanks!