A BOAT IS ROWED WITH A VELOCITY OF 8KM/H DUE NORTH STRAIGHT ACROSS A RIVER WHICH IS FLOWING AT 6 KM/H DUE EAST. find the magnitude of the resultant velocity in KM/H
To find the magnitude of the resultant velocity, you can use the Pythagorean Theorem. The resultant velocity is the vector sum of the boat's velocity and the river's velocity.
Given:
Boat's velocity = 8 km/h due north
River's velocity = 6 km/h due east
1. Draw a diagram to represent the velocities as vectors:
- Draw a vector pointing north with a length of 8 units to represent the boat's velocity.
- Draw a vector pointing east with a length of 6 units to represent the river's velocity.
- The angle between the boat's velocity and the resultant velocity is 90 degrees.
2. Now, draw a vector from the beginning of the boat's velocity to the end of the river's velocity. This represents the resultant velocity.
3. Use the Pythagorean Theorem to find the magnitude of the resultant velocity:
- The length of the boat's velocity vector is 8 units (since its velocity is 8 km/h due north).
- The length of the river's velocity vector is 6 units (since its velocity is 6 km/h due east).
- The length of the resultant velocity vector is unknown, denoted by 'v'.
- Apply the Pythagorean Theorem: v^2 = 8^2 + 6^2.
4. Solve for 'v':
- v^2 = 64 + 36
- v^2 = 100
- Taking the square root of both sides: v = √100 = 10.
Therefore, the magnitude of the resultant velocity is 10 km/h.
To find the magnitude of the resultant velocity, we need to use vector addition. The boat's velocity and the river's velocity can be represented as vectors.
Let's break down the given information:
- The boat's velocity due north is 8 km/h.
- The river's velocity due east is 6 km/h.
To find the resultant velocity, we need to add these two vectors together. Since the boat's velocity is due north and the river's velocity is due east, the two vectors are perpendicular to each other. Thus, we can use the Pythagorean theorem to find the magnitude of the resultant velocity.
The Pythagorean theorem states that the square of the hypotenuse (resultant velocity) is equal to the sum of the squares of the other two sides (boat's velocity and river's velocity).
Using the Pythagorean theorem, we have:
(resultant velocity)^2 = (boat's velocity)^2 + (river's velocity)^2
Substituting the given values:
(resultant velocity)^2 = (8 km/h)^2 + (6 km/h)^2
Calculating:
(resultant velocity)^2 = 64 km²/h² + 36 km²/h²
(resultant velocity)^2 = 100 km²/h²
Taking the square root of both sides to find the magnitude of the resultant velocity:
resultant velocity = √(100 km²/h²)
resultant velocity = 10 km/h
Therefore, the magnitude of the resultant velocity is 10 km/h.
Vr = sqr
t
Vr = Sqrt(8^2+6^2) =
9