A swimmer aims straight at the far bank of a flowing river and never corrects her heading. What happens to her motion over the riverbed?
Two identical boats aim straight at the far bank of a 100 m river, both moving at 4 m/s through the water. One crosses on a still day. The other crosses in a 3 m/s current that carries it far downstream. Which boat reaches the far bank first?
It looks like the drifting boat should lose time, because it travels a longer path. Follow the motion toward the far bank on its own, one direction at a time.
The current points downstream. The boat's motion toward the far bank is perpendicular to it. The current adds nothing toward the far bank and takes nothing away.
So each boat closes the 100 m to the far bank at the same 4 m/s:
crossing time = 100 m ÷ 4 m/s = 25 s
The current still matters. It decides where the drifting boat lands, well downstream of the other boat. It cannot change when the boat arrives.
A canoe aims straight at the far bank of a 50 m river at 2.5 m/s through the water, in a 1.8 m/s current. Calculate the crossing time.
Write down the values in the question:
river width = 50 m
speed toward the far bank = 2.5 m/s
current = 1.8 m/s, perpendicular to the crossing: it does not enter
crossing time = ?
Write down the equation:
crossing time = width ÷ speed toward the far bank
Substitute in the values:
crossing time = 50 m ÷ 2.5 m/s
Simplify:
crossing time = 20 s
A raft aims straight at the far bank of a 60 m channel at 2.0 m/s through the water, in a 1.5 m/s current. Enter the crossing time in s.
A kayaker crosses the same river twice at the same speed through the water, aimed straight at the far bank: once on a still day, once in a strong current. Which crossing takes longer?
A motorboat aims straight at the far bank at a steady speed through the water. Dario says that if the current speeds up, the motorboat will take longer to reach the far bank. Is he correct?
The independence of perpendicular motions returns in the projectiles topic. There, the same idea splits a thrown ball's motion into two separate one-dimensional problems.
A paddleboarder aims perpendicular to a steady current and reaches the far bank in the same time as on a still day. Why does the current leave the crossing time unchanged?
A swimmer aims straight at the far bank of a 72 m river at 1.8 m/s through the water, in a 2.4 m/s current. Enter the crossing time in s.
A blimp crosses a valley at a steady airspeed, headed perpendicular to a crosswind. What does the crosswind change?