Answer :
Final Answer:
The resultant velocity of the boat, considering both its original velocity and the current, is 34.1 km/h. So, the correct option is b).
Explanation:
To find the resultant velocity, we use the vector addition of the boat's original velocity and the velocity of the current. Given that the boat's original velocity is 30 km/h northeast and the current's velocity is 10 km/h southeast, we apply vector addition to determine the resultant velocity. Calculating the resultant velocity using vector addition, we find it to be 34.1 km/h.
In vector addition, the boat's original velocity and the current's velocity are represented as vectors, each with magnitude and direction. By adding these vectors using appropriate mathematical operations, we obtain the resultant velocity vector, representing the combined effect of both velocities.
Considering the boat's original velocity as one vector and the current's velocity as another, we determine their resultant vector through geometric addition, which accounts for both magnitude and direction. This process yields the final velocity of the boat, considering both its original motion and the influence of the current.
The resultant velocity provides a comprehensive understanding of the boat's movement, incorporating both its inherent speed and the impact of external factors like the current. This calculation is crucial for navigational purposes, aiding in determining the most efficient routes and estimating travel times accurately.
So, the correct option is b).