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Login Register. Share Facebook Pinterest Twitter 0. Description Boat dock RPG map symbol vector illustration. License Public Domain. More about SVG Size 0. Related SVG images. 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 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. That decision emerges from one's conceptual understanding or unfortunately, one's misunderstanding of the complex motion that is occurring.
The motion of the riverboat can be divided into two simultaneous parts - a motion in the direction straight across the river and a motion in the downstream direction. These two parts or components of the motion occur simultaneously for the same time duration which was 20 seconds in the above problem.
The decision as to which velocity value or distance value to use in the equation must be consistent with the diagram above. The boat's motor is what carries the boat across the river the Distance A ; and so any calculation involving the Distance A must involve the speed value labeled as Speed A the boat speed relative to the water. Similarly, it is the current of the river that carries the boat downstream for the Distance B ; and so any calculation involving the Distance B must involve the speed value labeled as Speed B the river speed.
Together, these two parts or components add up to give the resulting motion of the boat. That is, the across-the-river component of displacement adds to the downstream displacement to equal the resulting displacement. And likewise, the boat velocity across the river adds to the river velocity down the river to equal the resulting velocity. Now to illustra te an important point, let's try a second example problem that is similar to the first example problem.
Make an attempt to answer the three questions and then click the button to c heck your answer. The resultant velocity can be found using the Pythagorean theorem. It is. An import ant concept emerges from the analysis of the two example problems above. In fact, the current velocity itself has no effect upon the time required for a boat to cross the river.
The river moves downstream parallel to the banks of the river. As such, there is no way that the current is capable of assisting a boat in crossing a river. While the increased current may affect the resultant velocity - making the boat travel with a greater speed with respect to an observer on the ground - it does not increase the speed in the direction across the river. The component of the resultant velocity that is increased is the component that is in a direction pointing down the river.
It is often said that "perpendicular components of motion are independent of each other. The time to cross the river is dependent upon the velocity at which the boat crosses the river. It is only the component of motion directed across the river i. The component of motion perpendicular to this direction - the current velocity - only affects the distance that the boat travels down the river.
This concept of perpendicular components of motion will be investigated in more detail in the next part of Lesson 1. Determine the resultant velocity of the plane magnitude only if it encounters a. If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore? NOTE: the direction of the resultant velocity like any vector is expressed as the counterclockwise angle of rotation from due East.
If the width of the river is meters wide, then how much time does it take the boat to travel shore to shore? NOTE: the direction of the resultant velocity like any vector is expressed as the counterclockwise direction of rotation from due East.
It would require the same amount of time as before 20 s. Changing the current velocity does not affect the time required to cross the river since perpendicular components of motion are independent of each other. Note that an alteration in the current velocity would only affect the distance traveled downstream and the resultant velocity. Physics Tutorial. What Can Teachers Do My Cart Subscription Selection. Student Extras. See Answer a.
What is the resultant velocity of the motorboat? What distance downstream does the boat reach the opposite shore?
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