Question

A boat heads directly eastward across a pier at 12 meters per second. If the current in the river is flowing
at 5.0 meters per second due south, what is the magnitude of the boat's resultant velocity

Answer 1

Answer: 13 m/s

Explanation: The two vectors form a 5-12-13 right triangle. the magnitude of their resultant is the hypotenuse, which is 13 m/s.

Answer 2

The magnitude of the boat's resultant velocity (V) is 13 meters per second.

The velocity (v₁) of the boat heading in the eastward direction is in +ve (x-direction).

The velocity (v₂) of the current flowing in the south direction is in -ve (y-direction).

The magnitude of the boat's resultant velocity (V) can be determined by using the Pythagoras' rule:

∴

V² = V₁² + V₂²

V² = (12 m/s)² + (-5.0 m/s)²

$\mathbf{V = \sqrt{(12 m/s)^2 + (-5.0 m/s)^2}}$

$\mathbf{V = \sqrt{(144 m/s) + (25m/s)}}$

$\mathbf{V = \sqrt{(169 \ m/s) )}}$

V = 13 m/s

Therefore, we can conclude that the magnitude of the boat's resultant velocity (V) is 13 meters per second.

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