River Boat Problems Byjus Effect
08.09.2020
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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 River Boat Problems Byjus Effect 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 River Boat Problems Byjus Effect 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 River Boat Problems Byjus Effect distance corresponds to Average Speed B on the diagram above i.
The mathematics of River Boat Problems Byjus Effect the above problem is no more difficult than dividing or multiplying two numerical quantities River Boat Problems Byjus Effect 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 River Boat Problems Byjus Effect River Boat Problems Byjus Effect the complex motion that is occurring. The motion of the riverboat can be divided River Boat Problems Byjus Effect into two simultaneous parts - a motion in the direction straight across the river River Boat Problems Byjus Effect River Boat Problems Byjus Effect 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 River Boat Problems Byjus Effect above problem.
The decision as to which velocity value or distance value to use River Boat Problems Byjus Effect River Effect Byjus Boat Problems in the equation must be consistent with the diagram above. The boat's motor is Effect Boat Byjus Problems River 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 River Boat Problems Byjus Effect River Boat Problems Byjus Effect boat speed relative to the water.
Similarly, it is the current of the river Boat Effect Problems Byjus 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 Boat Byjus River Effect Problems displacement to equal the resulting displacement. And likewise, the boat velocity across the river River Boat Problems Byjus Effect 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 River Boat Problems Byjus Effect 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 River Boat Problems Byjus Effect from the analysis of the two example problems above. In fact, the current velocity River Boat Problems Byjus Effect itself has no effect upon the time required for a boat to cross the River Boat Problems Byjus Effect River Boat Problems Byjus Effect river.
The river moves downstream parallel to the banks of the river. As such, River Boat Problems Byjus Effect River Boat Problems Byjus Effect River Boat Problems Byjus Effect River Boat Problems Byjus Effect 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 River Boat Problems Byjus Effect 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 River Boat Problems Byjus Effect River Boat Problems Byjus Effect 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 River Boat Problems Byjus Effect River Boat Problems Byjus Effect 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 River Boat Problems Byjus Effect River Boat Problems Byjus Effect 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 River Boat Problems Byjus Effect 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 River Boat Problems Byjus Effect 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 River Boat Problems Byjus Effect Tutorial. What Can Teachers Do My Cart Subscription Selection. Student Extras.
See Answer a. He River Boat Problems Byjus Effect should swim in a direction? The velocity of the man in still water is equal to the relative velocity of the man w. Hence, the man takes the River Boat River Boat Problems Byjus Industries Problems Byjus Effect shortest time when he swims perpendicular to the river velocity i. Problem: A boat must get from point A to point B on the opposite bank of the River Boat Problems Byjus Effect river moving along a straight line AB that makes degree angle with the flow River Boat Problems Byjus Effect direction.
If distance AB is 2. The velocity of the boat relative to the ground should be along the line AB. Question: To cross a river in minimum time, your speed relative to the water should be perpendicular to the river flow.River Boat Problems Byjus Effect River Boat Problems Byjus Effect
At what angle to the stream direction must the boat move to minimize drifting? Solution: The drift is zero if boat reaches directly opposite point. The boat cannot cross the river to an exactly opposite point. Exercise: A boat must get from River Boat River Boat Problems Byjus Guide Problems Byjus Effect point A to point B on the opposite bank of the river. The distances River Boat Problems Byjus Effect BC and AC are equal. What is the minimum speed of the boat relative to the water? Exercise: A man can swim with a speed of 4.
How long does he take to cross a river 1. How far down the river does he go when he reaches the other bank? Two swimmers leave point A River Boat Problems Byjus Effect River Boat Problems Byjus Effect on one bank of the river to reach point B lying right across on River Boat Problems Byjus Effect the other bank. One of them crosses the river along the straight line AB River Boat Problems Byjus Effect River Boat Problems Byjus Effect while the other swims at right angles to the stream and then walks the distance that he has been carried away by the stream to get to point B.
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