Boat Water Speed
Posted on | September 10, 2010 | 2 Comments
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Boat Water Speed
what is the speed of the boat in still water?
the current in a stream moves at a speed of 10 km/h. A boat travels 38 km upstream and 38 km downstream in a total time of 9 hr.
Can someone please help me to set this up correctly and figure this out......the total time is throwing me off!
Total time of travel t is equal to the time upstream t1 plus the time downstream t2.
t=t1+t2
Since S is the distance traveled in one direction we have
t1=S/V1
t2=S/V2
Let
V' - Speed of the boat in still water
Vs - Speed of the stream
Then
Upstream
V1= V'- Vs
Downstream
V2= V' + Vs
Does that help? Need more?
t= S/(V'- Vs) + S/(V' + Vs)
S/t= (V'- Vs)(V' + Vs) / [(V'- Vs) + (V' + Vs)]
S/t= (V'- Vs)(V' + Vs) / [2V']
S/t= (V'^2- Vs^2) / [2V']
2V' S/t= V'^2- Vs^2
Now we have a quadratic equation and we need to solve for V'
V'^2 - 2V' S/t - Vs^2=0 or
V'^2 - 2(38/9) V' - 100=0
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Worlds Fastest Boat (all 4)
if the flow rate of the current in a straight river is a greater than the speed of a boat in the water,the boa
t cannot make a trip directly across the river.prove this statement.
The motion of the boat straight across is a vector made of 2 component vectors. Vector "A" would be the relative motion across the river. C1 the current "downstream" and C2 the motion of the vessel within the stream.
Since the speed of the vessel is not even enough to "hold" against the current, the boat will be moved downstream. The downstream motion will be faster once part of the boat propulsion is used to get across the river.
Comments
2 Responses to “Boat Water Speed”
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December 25th, 2010 @ 12:11 am
Have you ever changed the water pump impeller? It could be in a marginal state right now. Or the water intake could be partially blocked. Thermostat checked?
May 26th, 2011 @ 11:41 am
Let α be the reference angle the boat runs from P to Q with the opposite direction of the river flow, and β be the angle from Q to P with the direction of the river flow.
Since the time from P to Q is twice the time from Q to P, twice the speed from P to Q is equal to the speed from Q to P.
2(2vcosα – v) = 2vcosβ+v……(1) parallel to flow direction
2(2vsinα) = 2vsinβ……(2) perpendicular to flow direction
Cancel v,
4cosα = 2cosβ+3……(1)*
4sinα = 2sinβ……(2)*
(1)*^2+(2)*^2:16 = 4+12cosβ+9
=> cosβ = 1/4, sinβ = √(15/16)
t = 3t(from Q to P) = 3a/v(┴) = 3a/[2vsinβ] = 3a/[2v√(15/16)] = 2a√15/(5v)