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3 years ago

12

A boat crosses a 200m wide river at 3m/s, north relative to water. The river flows at 1m/s as shown. What is the velocity of the

boat as observed by a stationary observer on the river back from the boat departed?

1 answer:

Xelga [282]3 years ago

3 0

Answer:

The resultant velocity = 3.16 m/s

Explanation:

Since the boat is moving North of the direction of the riverflow, the river would either be flowing westward or Eastward. The two motions form a right angle triangle with the resultant velocity being the hypotenuse of the traingle.

The resultant velocity will be given as ;

R² = B² + r²

Where B is the velocity of the boat and r is the velocity of the river

R² = 3² + 1²

R² = 10

R = √10 = 3.16 m/s

Therefore, the resultant velocity = 3.16 m/s

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By making some algebraic handling:

$\frac{v(0)}{x(0)} = -\omega' \tan \phi$

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$\phi = \tan^{-1}\left[- \frac{1}{\omega'}\cdot \frac{v(0)}{x(0)}\right]$

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