Question

A sail boat sails at a heading of 72 degrees with a velocity of 20.0 km/h. The boat sails in a current of 5.00 km/h at a heading of 25 degrees.
What is the actual velocity of the boat.

Answer 1

Answer on Question #74564-Physics-Mechanics-Relativity

A sail boat sails at a heading of 72 degrees with a velocity of $20.0\mathrm{km/h}$. The boat sails in a current of $5.00\mathrm{km/h}$ at a heading of 25 degrees.

What is the actual velocity of the boat?

Solution

The actual velocity of the boat is

$$V = V _ {b o a t} + V _ {c u r r e n t}$$ $$V _ {x} = 2 0 \cos 7 2 + 5 \cos 2 5 = 1 0. 7 1 \frac {k m}{h}$$ $$V _ {y} = 2 0 \sin 7 2 + 5 \sin 2 5 = 2 1. 1 3 \frac {k m}{h}$$ $$V = \sqrt {(1 0 . 7 1) ^ {2} + (2 1 . 1 3) ^ {2}} = 2 3. 7 \frac {k m}{h}$$ $$\theta = \tan^ {- 1} \frac {2 1 . 1 3}{1 0 . 7 1} = 6 3. 1 {}^ {\circ}$$

The actual velocity of the boat is $23.7\mathrm{km/h}$ at a heading of 63.1 degrees.

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