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The resultant velocity of the motorboat can be determined in the same manner as was done for the plane.

The resultant velocity of the boat is the vector sum of the boat velocity and the river velocity. Since the boat heads straight across the river and since the current is always directed straight downstream, the two vectors are at right angles to each other. Thus, the Pythagorean theorem can be used to determine the resultant velocity. What would be the resultant velocity of the motorboat i. The magnitude of the resultant can be found as follows:.

The direction of the resultant is the counterclockwise angle of rotation that the resultant vector makes with due East. This angle can be determined using a trigonometric function as shown below. Motorboat problems such as these are typically accompanied by three separate questions:. The first of these three questions was answered above; the resultant velocity of the boat can be determined using the Pythagorean theorem magnitude and a trigonometric function direction. The second and third of these questions can be answered using the average speed equation and a lot of logic.

The solution to the first question has already been shown in the above discussion. We will start in on the second question. The river is meters wide. That is, the distance from shore to shore as measured straight across the river is 80 meters. The time to cross this meter wide river can be determined by rearranging and substituting into the average speed equation.

The distance of 80 m can be substituted into the numerator. But what about the denominator? What value should be used for average speed? With what average speed is the boat traversing the 80 meter wide river?

Most students want to use the resultant velocity in the equation since that is the actual velocity of the boat with respect to the shore. And the diagonal distance across the river is not known in this case. If one knew the distance C in the diagram below, then the average speed C could be used to calculate the time to reach the opposite shore. Similarly, if one knew the distance B in the diagram below, then the average speed B could be used to Free Clipart Sailboat Vector 40 calculate the time to reach the opposite shore.

And finally, if one knew the distance A in the diagram below, then the average speed A could be used to calculate the time to reach the opposite shore. It requires 20 s for the boat to travel across the river. During this 20 s of crossing the river, the boat also drifts downstream. Part c of the problem asks "What distance downstream does the boat reach the opposite shore?

And once more, the question arises, which one of the three average speed values must be used in the equation to calculate the distance downstream? The distance downstream corresponds to Distance B on the above diagram. The speed at which the boat covers this distance corresponds to Average Speed B on the diagram above i. The mathematics of the above problem is no more difficult than dividing or multiplying two numerical quantities by each other. The mathematics is easy!

The difficulty of the problem is conceptual in nature; the difficulty lies in deciding which numbers to use in the equations. Nautical emblem set with sail around the world marine life lighthouse marine world descriptions. Deck of professional sailboat or racing yacht during competition on sunny and windy summer day, moving fast through waves and water, with spinnaker up.

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Freepik Editor Beta Free online template editor. Numbers below 20 indicate a lightweight racing boat; 20 to 30 indicates a coastal cruiser; 30 to 40 indicates a moderate bluewater cruising boat; 40 to 50 indicates a heavy bluewater boat; over 50 indicates an extremely heavy bluewater boat. The CSF compares beam with displacement since excess beam contributes to capsize and heavy displacement reduces capsize vulnerability. The boat is better suited for ocean passages vs coastal cruising if the result of the calculation is 2.

The lower the better. Under 2 - Slow, under powered. Toggle Navigation Menu Home. Hull Type:.




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