For one-dimensional relative motion problems like this one, we’ll generally use the formula

$\overline{){{\mathbf{v}}}_{\mathbf{P}\mathbf{A}}{\mathbf{=}}{{\mathbf{v}}}_{\mathbf{P}\mathbf{B}}{\mathbf{+}}{{\mathbf{v}}}_{\mathbf{B}\mathbf{A}}}$

For example, if a boat is being propelled along a river, the boat’s velocity relative to the ground is the *boat’s velocity** relative to the **river* **plus** the *river’s velocity** relative to the **ground*. It’s important to keep track of the signs, so make sure you clearly define a coordinate system!

Because the velocities are constant, we'll end up using the equation

$\overline{){\mathbf{x}}{\mathbf{=}}{\mathbf{v}}{\mathbf{t}}}$

In this problem, we’re asked to calculate both the time it takes someone to **walk** the distance between the two piers *twice at a constant speed*, and the time it takes someone to **row** that distance once __along ____with__ the current and once __against__ the current. We’re given the walking speed, *v*_{w}, which is relative to the ground; the speed of the boat relative to the water, *v*_{b}_{r}; and the speed of the river relative to the ground, *v*_{r}_{g}.

Two piers, A and B, are located on a river: B is 1500 m downstream from A. Two friends must make round trips from pier A to pier B and return. One rows a boat at a constant speed of 4.00 km/h relative to the water; the other walks on the shore at a constant speed of 4.00 km/h. The velocity of the river is 2.80 km/h in the direction from A to B.**(a)** How much time does it take the walker to make the round trip?**(b)** How much time does it take the rower to make the round trip?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Intro to Relative Velocity concept. You can view video lessons to learn Intro to Relative Velocity. Or if you need more Intro to Relative Velocity practice, you can also practice Intro to Relative Velocity practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Jerousek's class at UCF.