Sometimes we want to look at an object that is moving at an angle to a moving reference frame like a boat trying to cross a river. Remember from the two-dimensional motion lesson that we usually separate motion into the x-direction and the y-direction. In problems like these, we look instead at the direction of the current and the direction across the river. See another example by clicking on this link, The River Boat.

The two most common problems you will see are: If I point straight across the river, how far downstream will I end up? And what direction do I need to point to wind up directly across the river?

In the following animation, you set the velocity of the boat (both magnitude and direction) and the speed of the current.

The animations below show a boat crossing a 224 m wide river.

The velocity of the boat (both magnitude and direction) is 4 m/s. Notice that the boat never lands directly across from the initial starting point.

Animation 1: The speed of the current is 5 m/s.

To find the value of x, the distance the boat landed downstream:

V_across = 4 m/s

D_across = 224 m

d = vt or t = d/v

t = 224/4 = 56 seconds

V_current = 5 m/s

d_downstream = x

t = 56 seconds

d = vt = (5) (56) = 280 m

Animation 2: The speed of the current is 2 m/s.

Calculate the value of x, the distance downstream the boat landed.

Interactive popup. Assistance may be required.

Need a hint?

Find the time to cross, and then see how far downstream.

Interactive popup. Assistance may be required.

Check Your Answer

V_across = 4 m/s
d_across = 224 m
d = vt or t = d/v
t = 224/4 = 56 seconds
v_current = 2 m/s
d_downstream = x
t = 56 sec
d = vt = (2) (56) = 112 m

Now check your answer using the animation. Use the slider on the bottom to set the current to 2m/s in the applet, click start, and see what the x value is in the bottom of the window.

Problem 2:

Use the animation to determine the angle that makes the boat wind up exactly across the river.

Interactive popup. Assistance may be required.

Check Your Answer

120°