A ship moves due north at 100km/hr on a river flowing due east at 25km/hr .
Calculate the magnitude of it's resultant velocity
To find the magnitude of the resultant velocity, we can use the Pythagorean theorem, which states that the square of the hypotenuse (resultant velocity) of a right triangle is equal to the sum of the squares of the other two sides (velocities).
Let's define the northward velocity as "Vnorth" and the eastward velocity as "Veast". Given that the ship is moving due north at 100 km/hr and the river is flowing due east at 25 km/hr, we have:
Vnorth = 100 km/hr (northward velocity)
Veast = 25 km/hr (eastward velocity)
Using the Pythagorean theorem, we can calculate the magnitude of the resultant velocity (Vresultant) as follows:
Vresultant² = Vnorth² + Veast²
Vresultant² = (100 km/hr)² + (25 km/hr)²
Vresultant² = 10000 km²/hr² + 625 km²/hr²
Vresultant² = 10625 km²/hr²
To find the magnitude of the resultant velocity, we take the square root of both sides:
Vresultant = √(10625 km²/hr²)
Vresultant ≈ 103.06 km/hr
Therefore, the magnitude of the ship's resultant velocity is approximately 103.06 km/hr.
To find the magnitude of the resultant velocity of the ship, we can use the Pythagorean Theorem because the ship's motion is along two perpendicular directions: north and east.
Let's break down the problem.
1. The ship's velocity due north is 100 km/hr.
2. The river's velocity due east is 25 km/hr.
Using these values, we can form a right triangle.
The northward velocity (ship's velocity) acts as the vertical side of the triangle, while the eastward velocity (river's velocity) acts as the horizontal side.
The magnitude of the resultant velocity can be found using the Pythagorean Theorem:
Resultant velocity^2 = (northward velocity)^2 + (eastward velocity)^2
Let's calculate it:
Resultant velocity^2 = (100 km/hr)^2 + (25 km/hr)^2
Resultant velocity^2 = 10000 km^2/hr^2 + 625 km^2/hr^2
Resultant velocity^2 = 10625 km^2/hr^2
Taking the square root of both sides, we get:
Resultant velocity = sqrt(10625) km/hr
Using a calculator or approximating, we find:
Resultant velocity ≈ 103.103 km/hr.
Therefore, the magnitude of the resultant velocity of the ship is approximately 103.103 km/hr.