A boy and a girl can both swim at 3.0 m.s. They jump into the same point of the river 66m across, with a current of 2.0 m/s [E]
a) The boy swims facing north at all times. What is his velocity relative to the ground?
b) The girl swims so that she ends up directly across from where she started. What is her velocity relative to the ground?
c) How long does it take each child to cross the river?
d) How far apart are they when they reach the other side of the river?
a) The boy swims facing north at all times. What is his velocity relative to the ground?
b) The girl swims so that she ends up directly across from where she started. What is her velocity relative to the ground?
c) How long does it take each child to cross the river?
d) How far apart are they when they reach the other side of the river?
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a) Sqrt.(3^2 + 2^2) = V relative to ground of 3.6m/sec. for the boy.
Direction = arctan (2/3) = 33.7 degrees east of north.
b) The girl swims pointing to the west of north.The angle she needs to swim at is arcsin (2/3) = 41.8 degrees west of north.
Her V relative to the ground is sqrt.(3^2 - 2^2) = 2.24m/sec., and direction is north.
c) The boy takes (66/3) = 22 secs. to swim across. The girl takes (66/2.24) = 29.46 secs.
d) The boy is swept east (22 x 2m/sec) = 44 metres. That is their distance apart.
Direction = arctan (2/3) = 33.7 degrees east of north.
b) The girl swims pointing to the west of north.The angle she needs to swim at is arcsin (2/3) = 41.8 degrees west of north.
Her V relative to the ground is sqrt.(3^2 - 2^2) = 2.24m/sec., and direction is north.
c) The boy takes (66/3) = 22 secs. to swim across. The girl takes (66/2.24) = 29.46 secs.
d) The boy is swept east (22 x 2m/sec) = 44 metres. That is their distance apart.