Two boats are on a lake. Boat A travels at 10 m/s east, and Boat B travels at 15 m/s north. Determine the velocity of Boat B relative to Boat A.
Guide On Rating System
Vote
To determine the velocity of Boat B relative to Boat A, we need to find the vector that represents the difference in their velocities.
Let's denote the velocity of Boat A as ππ΄ = 10 m/s east (positive x-axis direction), and the velocity of Boat B as ππ΅ = 15 m/s north (positive y-axis direction).
The velocity of Boat B relative to Boat A can be found by subtracting the velocity of Boat A from the velocity of Boat B:
ππ΅π΄ = ππ΅ - ππ΄
The x-component of ππ΅π΄ represents the east-west component of the velocity, and the y-component represents the north-south component of the velocity.
The x-component of ππ΅ is 0 m/s since Boat B is not moving horizontally.
The y-component of ππ΅ is 15 m/s.
The x-component of ππ΄ is 10 m/s.
Therefore, the x-component of ππ΅π΄ is 0 - 10 = -10 m/s (westward, as it is negative).
Thus, the velocity of Boat B relative to Boat A is ππ΅π΄ = (-10 m/s, 15 m/s).
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99