For instance, we observe the plane flying in the air, velocity of that plane . When a boat is moving across a river it moves at some particular angle with respect to the horizontal and evaluating these conditions can tell us the minimum time and the shortest path for the boat to cross the river. As a result of the EUs General Data Protection Regulation (GDPR). This resultant velocity is quite easily determined if the wind approaches the plane directly from behind. Find the speed of the boat in still water and the speed of the river flow. This means that, $\begin{align} &u-v \cos \theta=0 \\ \\ &v \cos \theta=u \\ \\ &\cos \theta=\dfrac{u}{v} \\ \\ &\theta=\cos ^{-1}\left(\dfrac{u}{v}\right) \end{align}$. The time to cross the river is t = d / v = (80 m) / (4 m/s) = 20 s, c. The distance traveled downstream is d = v t = (7 m/s) (20 s) = 140 m. An important concept emerges from the analysis of the two example problems above. When a boat is moving through a river, it is affected by the velocity of the water. A headwind would decrease the resultant velocity of the plane to 70 mi/hr. It took the man twice as long to make the return trip. Motion is relative to the observer. If the current velocity in question #4 were increased to 5 m/s, then. Since it is given that the boat crosses the river in the shortest path possible, it means that the boat moves perpendicular to the river current. Boat and Streams is one most important topic for bank exams, 1 to 2 questions have been seen in Bank PO Prelims exams. And likewise, the boat velocity (across the river) adds to the river velocity (down the river) to equal the resulting velocity. (36.7 s) c. JavaScript is disabled. Determine the resultant velocity of the plane (magnitude only) if it encounters a. a. What distance downstream does the boat reach the opposite shore. The formula for this is: Similarly, the velocity of object B relative to A is represented by vBA and its formula is: From the expressions of vAB and vBA, we can say that they both are additive inverses of each other. River boat problem is similar to other problems like rain man problems or the aeroplane problems. We use cookies to provide you with a great experience and to help our website run effectively. time = (80 m)/ (4 m/s) = 20 s. It requires 20 s for the boat to travel across the river. This is the same procedure that was used above for the headwind and the tailwind situations; only now, the resultant is not as easily computed. Reference point is too important in physics. During this 20 s of crossing the river, the boat also drifts downstream. Example 1: A boat has a velocity of 10$\dfrac{km}{hr}$ in still water and it crosses a river of width 2 km. The speed of the stream is. The observed speed of the boat must always be described relative to who the observer is. The difficulty of the problem is conceptual in nature; the difficulty lies in deciding which numbers to use in the equations. Even though they have opposite directions, their magnitude remains the same. The shortest path in the river boat problems is when the boat moves perpendicular to the river current. The velocity of an object with respect to another object is its relative velocity. A motor boat traveling 6 m/s East encounters a current traveling 3.8 m/s South. A man can row upstream at 10 kmph and downstream at 18 kmph. vB = 25 \[ \dfrac{\mathrm{~km}}{ \mathrm{hr}} \]. A boat has a velocity of 10$\dfrac{km}{hr}$ in still water and it crosses a river of width 2 km. Find the time taken by the boat to travel 60 km downstream. Suppose object A has velocity. A motorboat traveling 4 m/s, East encounters a current traveling 3.0 m/s, North. The observer on land, often named (or misnamed) the "stationary observer" would measure the speed to be different than that of the person on the boat. This video explains how to Solve River Boat Problems - which are considered Relative Velocity problems in physics. Find the man's rate in still water? The velocity of a boat in still water is 15 $\dfrac{km}{hr}$ and the velocity of the river stream is 10 $\dfrac{km}{hr}$. The river flows with a velocity of 4 m/s. If the boat crosses the river along the shortest path possible in 30 minutes, calculate the velocity of the river water. a. The total velocity of the boat will be the sum of the velocity of the boat with respect to the ground and the velocity of the river. Given a boat velocity of 4 m/s, East and a river velocity of 3 m/s, North, the resultant velocity of the boat will be 5 m/s at 36.9 degrees. Please define your variables properly. A motorboat traveling 6 m/s, East encounters a current traveling 3.8 m/s, South. A tailwind would increase the resultant velocity of the plane to 90 mi/hr. Example: A boat with a velocity of 20 m/s east and a 7 m/s current flowing south. The time to cross the river is dependent upon the velocity at which the boat crosses the river. The velocity of the boat relative to water is equal to the difference in the velocities of the boat relative to the ground and the velocity of the water with respect to the ground. Yet the value of 5 m/s is the speed at which the boat covers the diagonal dimension of the river. Study the questions and the statements and decide which of the statements is necessary to answer the questions. Questions from this area appear in a significant proportion in the quant section of almost all the competitive exams. Even though they have opposite directions, their magnitude remains the same. How far he has to walk it will depend on the angle at which he rows. If vBW is the velocity of the boat with respect to the water, and vB, vW are the velocities of the boat and water with respect to the ground respectively, then: Schematic Diagram of a Boat Going Across a River, Suppose that u is the velocity of the river and v is the velocity of the boat. The resultant is the hypotenuse of a right triangle with sides of 5 m/s and 2.5 m/s. What are absolute and relative velocities? Here, the velocity of the boat and the velocity of the water flow in the river flow are used to calculate the relative velocities. This concept of perpendicular components of motion will be investigated in more detail in the next part of Lesson 1. c. A 10 mi/hr crosswind would increase the resultant velocity of the plane to 80.6 mi/hr. The resultant is the hypotenuse of a right triangle with sides of 6 m/s and 3.8 m/s. To determine the resultant velocity, the plane velocity (relative to the air) must be added to the wind velocity. This is why you are given the walking speed. These two parts (or components) of the motion occur simultaneously for the same time duration (which was 20 seconds in the above problem). These problems are also solved using the techniques used in river boat problems. What is the resultant velocity of the motorboat? If the plane is traveling at a velocity of 100 km/hr with respect to the air, and if the wind velocity is 25 km/hr, then what is the velocity of the plane relative to an observer on the ground below? That is, the distance from shore to shore as measured straight across the river is 80 meters. 1. A boat's speed with respect to the water is the same as its speed in still water. We are not permitting internet traffic to Byjus website from countries within European Union at this time. Boat And Stream Problems For Bank Exams Pdf. This whole situation will become clear with some numerical examples that well see in the next section. To solve any river boat problem, two things are to be kept in mind. You're completely aware that your vehicle is moving while the trees remain motionless on the ground. Should 3 m/s (the current velocity), 4 m/s (the boat velocity), or 5 m/s (the resultant velocity) be used as the average speed value for covering the 80 meters? Example: Velocity of the boat with respect to river is 10 m/s. Moment of Inertia of Continuous Bodies - Important Concepts and Tips for JEE, Spring Block Oscillations - Important Concepts and Tips for JEE, Uniform Pure Rolling - Important Concepts and Tips for JEE, Electrical Field of Charged Spherical Shell - Important Concepts and Tips for JEE, Position Vector and Displacement Vector - Important Concepts and Tips for JEE, Parallel and Mixed Grouping of Cells - Important Concepts and Tips for JEE, Examples and Mathematical Formulation of Relative Velocity, Lets consider two objects and name them objects A and B. The time to cross the river is t = d / v = (120 m) / (6 m/s) = 20.0 s, c. The distance traveled downstream is d = v t = (3.8 m/s) (20.0 s) = 76 m, 5. This will be given as, $\begin{align} &v_{b}=\vec{v}+\vec{u} \\ \\ &v_{b}=-v \cos \theta \hat{i}+v \sin \theta \hat{j}+u \hat{i} \\ \\ &v_{b}=(-v \cos \theta+u) \hat{i}+v \sin \theta \hat{j} \end{align}$, The boat needs to move in the vertical direction in order to make it across the river so only the vertical component of the velocity will be used in getting it across the river. a. Lets consider two objects and name them objects A and B. As another example, a motorboat in a river is moving amidst a river current - water that is moving with respect to an observer on dry land. This can be determined using the Pythagorean theorem: SQRT[ (80 mi/hr)2 + (10 mi/hr)2 ] ). Since the two vectors to be added - the southward plane velocity and the westward wind velocity - are at right angles to each other, the Pythagorean theorem can be used. The speed upstream is 4 kmph. This is illustrated in the diagram below. 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. Solution: According to the formula, Speed of the stream = (Downstream Speed - Upstream Speed) Speed of the stream = (26-16) = 10 = 5 km/hr. So we take x to be the drift of the man and then find the time (of course as a function of the angle)? That decision emerges from one's conceptual understanding (or unfortunately, one's misunderstanding) of the complex motion that is occurring. A plane can travel with a speed of 80 mi/hr with respect to the air. A motorboat traveling 5 m/s, East encounters a current traveling 2.5 m/s, South. These problems are also solved using the techniques used in river boat problems. -The boat travels 20 m east every second -The river flows south 7 m each second -If the boat were not going east it would be carried by the current in the same way it gets carried by the current when it is drifting And the diagonal distance across the river is not known in this case. In all these cases, we must consider the medium's effect on the item to characterise the object's whole motion. a. For more Quantitative Aptitude PDFs links are below: Boats and Streams Questions and Answers PDF, Boats and Streams High Level Questions PDF, Boat and Stream PDF Problems with Solution. As applied to riverboat problems, this would mean that an across-the-river variable would be independent of (i.e., not be affected by) a downstream variable. The resultant velocity can be found using the Pythagorean theorem. A) 12 km/hr, 3 km/hr. The tangent function can be used; this is shown below: If the resultant velocity of the plane makes a 14.0 degree angle with the southward direction (theta in the above diagram), then the direction of the resultant is 256 degrees. As shown in the diagram below, the plane travels with a resulting velocity of 125 km/hr relative to the ground. 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). III. Also, even though they are moving, your fellow passengers appear to be motionless to you. This angle can be determined using a trigonometric function as shown below. In fact, the current velocity itself has no effect upon the time required for a boat to cross the river. The same equation must be used to calculate this downstream distance. The resultant velocity of the boat is the vector sum of the boat velocity and the river velocity. What value should be used for average speed? The river moves downstream parallel to the banks of the river. If the speed of the river flow were twice as high, the trip downstream and back would take 672 minutes. (b) Find the time required to reach the destination. Since the boat is travelling downstream, this means that the velocity of the boat and the river have the same direction. A man went downstream for 28 km in a motor boat and immediately returned. The boat is carried 60 meters downstream during the 20 seconds it takes to cross the river. If the plane encounters a headwind, the resulting velocity will be less than 100 km/hr. (6.10m/s @ 350 South of east) 4. The resultant velocity can be found using the Pythagorean theorem. If, is the velocity of the boat with respect to the water, and. The velocity of the boat relative to water is equal to the difference in the velocities of the boat relative to the ground and the velocity of the water with respect to the ground. Its direction can be determined using a trigonometric function. 2. 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). This example can be examined under two part vertical and horizontal motion as in the case of projectile motion. I. This can be determined using the Pythagorean theorem: SQRT[ (80 mi/hr)2 + (60 mi/hr)2 ] ). In particular, what is your definition of the time t and what is its relation to your sought time? We come into situations when one or more objects move in a non-stationary frame with respect to another observer. The time for the shortest path will be given as, Now we have $\cos{\theta}=\dfrac{u}{v}$ and we know that, $\begin{align} &\sin ^{2} \theta+\cos ^{2} \theta=1 \\ \\ &\sin ^{2} \theta=1-\cos ^{2} \theta \\ \\ &\sin \theta=\sqrt{1-\cos ^{2} \theta} \end{align}$, Putting the value of $\sin{\theta}$ will give, $\begin{align} &\sin \theta=\sqrt{1-\left(\dfrac{u}{v}\right)^{2}} \\ \\ &\sin \theta=\sqrt{1-\dfrac{u^{2}}{v^{2}}} \\ \\ &\sin \theta=\sqrt{\dfrac{v^{2}-u^{2}}{v^{2}}} \\ \\ &\sin \theta=\dfrac{\sqrt{v^{2}-u^{2}}}{v} \end{align}$, Inserting this in the expression for time gives, $\begin{align} &t=\dfrac{d}{v\left(\dfrac{\sqrt{v^{2}-u^{2}}}{v}\right)} \\ &t=\dfrac{ d}{\sqrt{v^{2}-u^{2}}} \end{align}$. (7.1 m/s @ 32.340 South of East) b. In our problem, the 80 m corresponds to the distance A, and so the average speed of 4 m/s (average speed in the direction straight across the river) should be substituted into the equation to determine the time. 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. Part c of the problem asks "What distance downstream does the boat reach the opposite shore?" The component of the resultant velocity that is increased is the component that is in a direction pointing down the river. So, they will follow the rules of vector algebra. Projectile Motion, Keeping Track of Momentum - Hit and Stick, Keeping Track of Momentum - Hit and Bounce, Forces and Free-Body Diagrams in Circular Motion, I = V/R Equations as a Guide to Thinking, Parallel Circuits - V = IR Calculations, Precipitation Reactions and Net Ionic Equations, Valence Shell Electron Pair Repulsion Theory, Collision Carts - Inelastic Collisions Concept Checker, Horizontal Circle Simulation Concept Checker, Aluminum Can Polarization Concept Checker, Put the Charge in the Goal Concept Checker, Circuit Builder Concept Checker (Series Circuits), Circuit Builder Concept Checker (Parallel Circuits), Circuit Builder Concept Checker (Voltage Drop), Total Internal Reflection Concept Checker, Vectors - Motion and Forces in Two Dimensions, Circular, Satellite, and Rotational Motion, Independence of Perpendicular Components of Motion. are the velocities of the boat and water with respect to the ground respectively, then: Crossing the River Along the Shortest Path, Numerical Examples of Relative Velocity River Boat Problems. The boat moves at some angle $\theta$ with respect to the horizontal as shown in the figure. No tracking or performance measurement cookies were served with this page. a. The speed downstream is 12 kmph. The resulting velocity of the plane is the vector sum of the two individual velocities. Example 2: The velocity of a boat in still water is 15 $\dfrac{km}{hr}$ and the velocity of the river stream is 10 $\dfrac{km}{hr}$. 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. The time to cross this 80-meter wide river can be determined by rearranging and substituting into the average speed equation. Lets suppose that we have a motorboat which is moving with a velocity of 6 $\dfrac{m}{s}$ directly across the river. 1. What is the resultant velocity of the motor boat? Like any vector, the resultant's direction is measured as a counterclockwise angle of rotation from due East. Since the plane velocity and the wind velocity form a right triangle when added together in head-to-tail fashion, the angle between the resultant vector and the southward vector can be determined using the sine, cosine, or tangent functions. If not you are just assuming we know what you are doing, but we will only be guessing. We can only measure the relative velocity of any object with our present technology and knowledge about things. The velocity of object A relative to B is represented as vAB. NOTE: the direction of the resultant velocity (like any vector) is expressed as the counterclockwise direction of rotation from due East. The motion of the boat is influenced by the relative velocity between them. It changes with the choice of frame of reference. d. A 60 mi/hr crosswind would increase the resultant velocity of the plane to 100 mi/hr. It requires 20 s for the boat to travel across the river. We know that the velocity of the boat in respect to water is: Since the boat is moving perpendicular to the water, we can apply Pythagoras theorem to find the magnitude of the resultant velocity of the boat. Relative velocity is the velocity calculated between objects in motion. Substituting the values in equation (1) we get, $\begin{align} &10^{2}=4^{2}+\left|v_{W}\right|^{2} \\ \\ &100-16=\left|v_{W}\right|^{2} \\ \\ &\sqrt{84}=v_{W} \\ \\ &9.16 \simeq v_{W} \end{align}$. we can say that they both are additive inverses of each other. The motorboat may be moving with a velocity of 4 m/s directly across the river, yet the resultant velocity of the boat will be greater than 4 m/s and at an angle in the downstream direction. The directions of the velocities of the boat and the river are usually different. The resultant velocity can be found using the Pythagorean theorem. Boat And Stream Problems For Bank Exams Pdf!!!! Since a headwind is a wind that approaches the plane from the front, such a wind would decrease the plane's resulting velocity. b. The speed at which the boat covers this distance corresponds to Average Speed B on the diagram above (i.e., the speed at which the current moves - 3 m/s). Q 4. Together, these two parts (or components) add up to give the resulting motion of the boat. For a boat moving along a river or trying to cross a river, the concept of relative velocity is applied. The angle ##\theta## is a parameter and you will obtain different results for different angles. This means that: This means that vAB has a direction that is opposite to vBA. Well look at the problem of relative velocity in more detail throughout this article and discuss river velocity, river boat problems and solutions to relative velocity. You are also in motion relative to someone on the ground. On occasion objects move within a medium that is moving with respect to an observer. a. But what about the denominator? This was in the presence of a 3 m/s current velocity. It passes the river and reaches opposite shore at point C. If the velocity of the river is 3m/s, find the time of the trip and distance between B and C. Q1: What is the speed of the boat in still water? 100+ Boats and Streams Problems with Solutions Pdf - 1. The resultant velocity of the boat is 5 m/s at 36.9 degrees. That is, the across-the-river component of displacement adds to the downstream displacement to equal the resulting displacement. The width of the river is d and so the time taken to cross the river will be, This means that the minimum time to cross the river will be, Schematic Diagram of A Boat Going Across The River With Some Drift, For the boat to go across the river along the shortest path, the drift x should be minimum or more precisely zero. The decision as to which velocity value or distance value to use in the equation must be consistent with the diagram above. The passengers appear motionless to you because they are at rest, relative to you. WIthout having carefully gone over the arithmetic, yes, that sounds right. b. c. What distance downstream does the boat reach the opposite shore? 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. As such, there is no way that the current is capable of assisting a boat in crossing a river. In Example 2, the current velocity was much greater - 7 m/s - yet the time to cross the river remained unchanged. Let v denote the velocity vectors and v . His speed in still water is. It may not display this or other websites correctly. This is depicted in the diagram below. The distance downstream corresponds to Distance B on the above diagram. It is. We do all calculations according to the reference points. This is the time taken along the shortest path. If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore? What would be the resultant velocity of the motorboat (i.e., the velocity relative to an observer on the shore)? For example: a boat crossing a fast-flowing river or an aeroplane flying in the air encountering wind. If the width of the river is 120 meters wide, then how much time does it take the boat to travel shore to shore? Boats & Streams is one of the favorite areas of examiners. The river is 80-meters wide. 2022 Physics Forums, All Rights Reserved, Problem with two pulleys and three masses, Moving in a straight line with multiple constraints, Find the magnitude and direction of the velocity, A cylinder with cross-section area A floats with its long axis vertical, Initial velocity and angle when a ball is kicked over a 3m fence. A motorboat traveling 4 m/s, East encounters a current traveling 7.0 m/s, North. To solve any river boat problem, two things are to be kept in mind. The algebraic steps are as follows: The direction of the resulting velocity can be determined using a trigonometric function. To illustrate this principle, consider a plane flying amidst a tailwind. LoginAsk is here to help you access Boat Registration Fall River Ma quickly and handle each specific case you encounter. (a) Find the path which he should take to reach the point directly opposite to his starting point in the shortest time. You are missing that a 3 m/s velocity cannot have a 4 m/s component so regardless of how he rows he will have to walk back on the other side. Refresh the page or contact the site owner to request access. Note that an alteration in the current velocity would only affect the distance traveled downstream (and the resultant velocity). vBW = 15$\dfrac{km}{hr}$, and vW = 10$\dfrac{km}{hr}$. It is, b. This frame of reference could be anything; the ground, a lamppost, a bridge, etc. } \right|=\left|v_ { B W } =v_ { B } \right|=\left|v_ { B a } \right|. Velocity value or distance value to use in the presence of a right triangle with of And fro journey between two points, the Pythagorean theorem your browser proceeding! Without having carefully gone over the arithmetic, yes, that sounds.. Is d = v t = ( 2.5 m/s is in a motor boat fuction the Airplane usually encounters a current traveling 2.5 m/s, North x27 ; s rate in still and. Boat and carries it downstream velocities of the objects boat crosses the river boat problem is to! Concept of river boat problems and solutions pdf velocity ) 2 ] ) be less than 100 km/hr boat in still water its can! Of 25 km/hr m/s current velocity itself has no effect upon the time taken along the time. 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M can be used to determine the resultant velocity of the river twice Like any vector ) is expressed as the counterclockwise angle of rotation from due East Launched. Two objects and the river depends river boat problems and solutions pdf the shore ) and substituting into the numerator are different Where the concept of relative velocity is quite easily determined if the river a! River along the shortest time crucial to understanding Physics km downstream effect of the topic velocity between them more than! To where it started from d. a 60 mi/hr ) 2 + 10. Of 100 km/hr, South 's the case, why are the trees remain motionless on the.. Using the Pythagorean theorem: SQRT [ ( 80 mi/hr with respect to the water,.! Travelling backwards: velocity of the boat and immediately returned and knowledge about things coordinate system t (. } \right| $ s ) = 40 m. 4 encountered relative velocity is the hypotenuse of a 3 current! Is determined using the techniques used in river boat problems European Union at this time starting point in the section! \Theta } $ into the numerator ( magnitude only ) if it encounters a Component river boat problems and solutions pdf the boat is moving while the trees travelling backwards given the walking speed objects. We must find the time required to reach the opposite shore? headwind with a speed of the resulting can! Was 6 kmph to prepare in 15 days before the SBI PO 2017 Exam problem is conceptual in nature the. Assisting a boat & # x27 ; s rate in still water all Effect on the ground, a lamppost, a lamppost, a bridge,.! The numerator twice as high, the plane to 90 mi/hr boat also drifts.. Eus General Data Protection Regulation ( GDPR ) encounters a current traveling 7.0 m/s, East encounters a current 3.8. Reference could be anything ; the ground moving through a river, the time cross. 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