Answer :
8 km/h +6km/h =14 km/h assuming that the boat is going the same direction as the current.
The Resultant Speed of boat rowed at 8km/hr directly across a river that flows at 6km/hr is 10km/hr
Given the data in the question;
Velocity of boat; [tex]V_m = 8km/hr[/tex]
Velocity of the flowing river; [tex]V_r = 6km/hr[/tex]
Resultant Velocity; [tex]V = ?[/tex]
Now, as illustrated in the diagram below, a right angled triangle is formed.
Now, to get the V, which is the resultant velocity or speed, we make use of the Pythagorean theorem:
[tex]c^2 = a^2 + b^2[/tex]
In our case,
[tex]V^2 = V_r^2 + V_m^2[/tex]
We find the square root of both sides
[tex]V = \sqrt{V_r^2 + V_m^2}[/tex]
Now, we substitute in our given values
[tex]V = \sqrt{(6km/hr)^2 + (8km/hr)^2}\\\\V = \sqrt{ (36km^2/hr^2) + ( 64 km^2/hr^2)\\[/tex]
[tex]V = \sqrt{100 km^2/hr^2[/tex]
[tex]V = 10km/hr[/tex]
Therefore, The Resultant Speed of boat rowed at 8km/hr directly across a river that flows at 6km/hr is 10km/hr
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