Question

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

Answer 1

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.