Kinematics in one direction - relative velocity word problem

[r26h]

Homework Statement

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?

Homework Equations

These equations were given by my instructor:
x=at²/2+v_it
x=v_avgt
v_f²=v_i²+2ax
v_f=v_i+at
gravity = 10 m/s²

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

 

[haruspex]

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

 

[r26h]

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

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