# Kinematics in one direction - relative velocity word problem

1. Sep 4, 2015

### r26h

1. The problem statement, all variables and given/known data
Danielle bikes at a steady rate of 4.0 m/s south along the bank of a river. Summer is rowing her kayak heading south down the river; she can row at a constant rate of 2.0 m/s in still water. There is a 5.0 meter wide bridge that spans the river and the bike trail.
a) If it takes Summer 0.75 seconds longer to go under the bridge, what is the velocity of the current?
b) What is Summer's velocity relative to Danielle's?
c) What is Summer's velocity relative to the shore?
d) What is Danielle's velocity relative to the river as it flows?

2. Relevant equations
These equations were given by my instructor:
x=at2/2+vit
x=vavgt
vf2=vi2+2ax
vf=vi+at
gravity = 10 m/s2

3. The attempt at a solution
a) to find how long it took Danielle to cross river, I made a proportion 4m/1s =1m/x. x=.25 seconds. It took Danielle 1.25 seconds to cross the river. 1.25+.75= 2 seconds for Summer to cross the river.

x=(Velocity of Summer + Velocity of current)(t)
5m=(2m/s + Velocity of current)(2s)
5/2 m/s = 2 m/s + Velocity of current
1/2 m/s = Velocity of the current

b) Velocity of (Summer + Current )- Velocity of Danielle = relative velocity
2.5 m/s - 4 m/s = -1.5 m/s

c) Velocity of (Summer + Current) - 0 = relative velocity
2.5 m/s - 0 = 2.5 m/s

d) Velocity of Danielle - Velocity of River = relative velocity
4 m/s - .5 m/s = 3.5 m/s

2. Sep 4, 2015

### haruspex

That all looks right, except that nobody crosses the river.

3. Sep 4, 2015

### r26h

Sorry, I meant 'cross the bridge'. Thank you