A ship move due North at 100km-1 on a river flowing due east at 25-2.calculate the magnitude of the resultant velocity of the ship?
sqrt (100^2 + 25^2) = sqrt (10,625) = 103.08
100-2+25-2
10000+625=10625=103.08
103.08+100+25=228.08
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To calculate the magnitude of the resultant velocity of the ship, we can use the concept of vector addition. Given that the ship is moving due North at a speed of 100 km/h and the river is flowing due East at a speed of 25 km/h, we need to determine the combined effect of these two velocities.
To do this, we can create a right-angled triangle where the Northward velocity of the ship is the vertical leg and the Eastward velocity of the river is the horizontal leg. The resultant velocity will be the hypotenuse of this triangle. Using the Pythagorean theorem, we can find the magnitude of the resultant velocity.
Let's denote the Northward velocity of the ship as V_ship = 100 km/h and the Eastward velocity of the river as V_river = 25 km/h. Using these values, we can apply the Pythagorean theorem:
Resultant velocity^2 = V_ship^2 + V_river^2
Resultant velocity^2 = (100 km/h)^2 + (25 km/h)^2
Resultant velocity^2 = 10,000 km^2/h^2 + 625 km^2/h^2
Resultant velocity^2 = 10,625 km^2/h^2
Taking the square root of both sides to solve for the magnitude of the resultant velocity:
Resultant velocity = √(10,625 km^2/h^2)
Resultant velocity ≈ √10,625 km/h
Resultant velocity ≈ 103.1 km/h (rounded to one decimal place)
Therefore, the magnitude of the resultant velocity of the ship is approximately 103.1 km/h.