A river flows at 2m/s the velocity of a ferry relative totle shore is 4m/s at right angles to the current what is the velocity of the ferry relative to the current
To determine the velocity of the ferry relative to the current, you can use vector addition.
The velocity of the river current is given as 2 m/s, and the velocity of the ferry relative to the shore is given as 4 m/s at right angles to the current.
To find the velocity of the ferry relative to the current, we can use the Pythagorean theorem to find the resultant velocity:
Resultant velocity^2 = (Velocity of the river current)^2 + (Velocity of the ferry relative to the shore)^2
Substituting the given values, we have:
Resultant velocity^2 = (2 m/s)^2 + (4 m/s)^2
Resultant velocity^2 = 4 m^2/s^2 + 16 m^2/s^2
Resultant velocity^2 = 20 m^2/s^2
Taking the square root of both sides to solve for the resultant velocity, we have:
Resultant velocity = √(20 m^2/s^2)
Resultant velocity ≈ 4.47 m/s
Therefore, the velocity of the ferry relative to the current is approximately 4.47 m/s.
To find the velocity of the ferry relative to the current, you need to use vector addition.
First, let's break down the velocities into their components. The river flows at a velocity of 2m/s, and the velocity of the ferry relative to the shore is 4m/s at a right angle to the current.
The velocity of the river can be represented as Vr = 2m/s.
The velocity of the ferry relative to the shore can be represented as Vfs = 4m/s.
To find the velocity of the ferry relative to the current, we need to add the two vectors together.
Let's assume that the direction of the current is the positive x-axis and the direction of the ferry's velocity relative to the shore is the positive y-axis.
Therefore, the velocity of the ferry relative to the current can be represented as Vfc = Vfs + Vr.
Since the two vectors are perpendicular to each other, we can use the Pythagorean theorem to find the magnitude of the resulting vector. The magnitude of the vector can be represented as:
|Vfc| = √(Vfs^2 + Vr^2)
Plugging in the given values:
|Vfc| = √(4^2 + 2^2) = √(16 + 4) = √20 = 2√5
Therefore, the velocity of the ferry relative to the current is 2√5 m/s.