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Relative Velocity
River with current. Label upstream and downstream
A upstream , B downstream
Ex 1) A boat's speed in still water is 1.85 m/s.
If the boat is to travel
directly across a river whose current is 1.20 m/s, at what upstream
angle must the boat head?
sinӨ = [1.20 m/s]/[1.85 m/s]
Ө = 40.5°
upstream
Crossing a River
When a boat crosses a river,
which component(s) are affected. V_{x}? V_{y}?
Only V_{x }changed
when boat crosses river
V_{r} = Velocity of river
V_{bx} = Boat's x velocity
V_{by} = Boat's y velocity
Find V_{x}'
Vx' =
Vx' =
Vx'=
Path B
V_{x}' = Vr
Path A
V_{x}' = V_{bx}  V_{r}
Path C
V_{x}' = V_{bx} + V_{r}
Downstream
or straight across
V_{x} increased
Upstream
V_{x} decreased
V_{x}' = V_{boat} +/ V_{river}
V_{y} = V_{yboat}_{
V}^{'2}
= V_{x}'^{2} + V_{y}^{2}
d_{x} , d_{y}?
d_{y} = V_{y}t
d_{x} = (V_{boat} + V_{river})t
Ex 2) A boat's speed in still water is of 10. m/s. The
boat moves downstream across the river at an angle of 37 degrees from the shoreline
and reaches opposite shore at point B.
If the velocity of the river is 3.0 m/s, find the time of the trip and
distance between A and B. The width of the river is 36 m.
d_{x} = V_{x}t
Finding t
d_{y} = 36m
d_{y} = V_{y}t = VsinӨt
= 36 m
36 m = 10 m/s[sin37]t
t = 6 sec
d_{x} = V_{x}t
Finding V_{x}
V_{x} = V_{x} boat + V_{x} river
V_{x} of
Boat
V_{x} = 10 m/s[cos37]
= 8 m/s
V_{x} River = 3 m/s
V_{x} = 11 m/s
t = 6 sec
d_{x} = V_{x}t
d_{x} = 66 m
Intro to
Circular Motion
ŠTony Mangiacapre.,
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