Two canoeists in identical canoes exert the same effort paddling and hence maintain the same speed relative to the water. one paddles directly upstream (and moves upstream), whereas the other paddles directly downstream. with downstream as the positive direction, an observer on shore determines the velocities of the two canoes to be −1.2m/sand +2.9m/s, respectively. (a)what is the speed of the water relative to the shore? (b)what is the speed of each canoe relative to the water?

a) speed of water relative to shore = 0.85 m/s

b) speed of each canoe relative to the water =  2.05 m/s

Explanation:

Let the speed of the canoeists be 'v'

and,

the speed of stream relative to shore be 'u'

therefore,

for the canoeist padding upstream

u - v = - 1.2 m/s (1)

and,

for the canoeist padding downstream

u + v = 2.9 m/s  (2)

on adding equation (1) and (2), we get

   u - v = - 1.2

+  u + v = 2.9

  2u + 0 = 1.7

or

u = 0.85 m/s

substituting u in equation 2 we get

0.85 + v = 2.9

or

v = 2.05 m/s

Hence,

a) speed of water relative to shore = 0.85 m/s

b) speed of each canoe relative to the water =  2.05 m/s

scientific laws are the result of testing theories and proving them to be facts.