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(PHYS126)[2011](s)quiz~3030^_10056.pdf
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PHYS126 Quiz 1 17-2-2011 Time: 10min Name: Student ID:
1. Let c = speed of the swimmer in still water v = velocity of water current L = distance between starting and end points
t1 = roundtrip time swimming along the river current
t2 = roundtrip time across the river current
Using classical velocity addition formula,
(a)
express t1 in terms of c, v and L
(b)
express t2 in terms of c, v and L
1
(c)
show in general, t1 ..t2 , where ..
2
v
1. 2
c
You should draw vector diagrams to help your derivation and show your steps explicitly. Points will be given upon how well you present your answer.
(Hint: Swimming across must be at an angle to balance the current flow, i.e. v = c sin ) (10 marks)
Solution to Quiz 1
Round trip of total distance Round trip of total distance
2L, along river 2L, across river
Velocity of swimmer relative to ground
L L 2cL
(a) Along the water current, t1 ... 22
cv. c . vc . v 2L
(b) Across the water current, t2 . c2 . v2
2cL
t c1
1 c2 . v2
(c) .. .
.. , so t .. t .
2L
22
2 12
t2 c . vv
22 1.
c . v c2