a boat travels in still water at 2m/s. It is rowed across a river that flows at 1m/s. Determine the resultant velocity of the boat
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To determine the resultant velocity of the boat, we need to consider the vector addition of the velocities of the boat in still water and the velocity of the river.
To do this, we can use the concept of vector addition. Let's represent the velocity of the boat in still water as "v_boat" and the velocity of the river as "v_river."
Given that the boat travels at 2 m/s in still water (v_boat = 2 m/s) and the river flows at 1 m/s (v_river = 1 m/s), we can determine the resultant velocity by adding these two vectors together.
To perform vector addition, we add the magnitudes of the two vectors in the direction of the resultant vector. In this case, since the river flows sideways with respect to the boat's forward direction, we can treat the velocities as perpendicular to each other.
Using the Pythagorean theorem, we can find the magnitude of the resultant velocity (v_resultant) as:
v_resultant = sqrt(v_boat^2 + v_river^2)
= sqrt((2 m/s)^2 + (1 m/s)^2)
= sqrt(4 m^2/s^2 + 1 m^2/s^2)
= sqrt(5 m^2/s^2)
≈ 2.24 m/s
Therefore, the resultant velocity of the boat is approximately 2.24 m/s.