However, to someone on the ground who isnt moving, your fellow passengers are in motion, relative to them. It is confusing at first, but is indeed an important topic for JEE Main. This can be determined using the Pythagorean theorem: SQRT[ (80 mi/hr)2 + (60 mi/hr)2 ] ). It may not display this or other websites correctly. 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? A boat's speed with respect to the water is the same as its speed in still water. This video explains how to Solve River Boat Problems - which are considered Relative Velocity problems in physics. Let be the width of the river and x be the drifting of the boat. The velocity of a boat in still water is 15 $\dfrac{km}{hr}$ and the velocity of the river stream is 10 $\dfrac{km}{hr}$. This concept of perpendicular components of motion will be investigated in more detail in the next part of Lesson 1. The river current influences the motion of the boat and carries it downstream. This was in the presence of a 3 m/s current velocity. Net Force (and Acceleration) Ranking Tasks, Trajectory - Horizontally Launched Projectiles, Which One Doesn't Belong? You cannot access byjus.com. Of course, it's the time taken to cross the river. What value should be used for average speed? The effect of the wind upon the plane is similar to the effect of the river current upon the motorboat. As a result of the EUs General Data Protection Regulation (GDPR). 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). -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 The decision as to which velocity value or distance value to use in the equation must be consistent with the diagram above. Find the time taken by the boat to travel 60 km downstream. c. The distance traveled downstream is d = v t = (2.5 m/s) (16.0 s) = 40 m. 4. A tailwind would increase the resultant velocity of the plane to 90 mi/hr. This is where the concept of relative velocity comes into play. c. A 10 mi/hr crosswind would increase the resultant velocity of the plane to 80.6 mi/hr. 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? 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. This is illustrated in the diagram below. WIthout having carefully gone over the arithmetic, yes, that sounds right. Boat and Streams is one most important topic for bank exams, 1 to 2 questions have been seen in Bank PO Prelims exams. In a to and fro journey between two points, the average speed of the boat was 6 kmph. Solution Problem-1 by Sketch of Knowledge Strategy Helmi Abdullah, Program Studi Pendidi kan Fisika Universitas Negeri Makassar 2 If the boat requires 100s to cross the path AB, then the buoy has . And likewise, the boat velocity (across the river) adds to the river velocity (down the river) to equal the resulting velocity. 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. A headwind would decrease the resultant velocity of the plane to 70 mi/hr. For a better experience, please enable JavaScript in your browser before proceeding. 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. Homework Equations. What would be the resultant velocity of the motorboat (i.e., the velocity relative to an observer on the shore)? Relative velocity is the velocity calculated between objects in motion. Velocity of the moving objects with respect to other moving or stationary object is called "relative velocity" and this motion is called "relative motion". 100+ Boats and Streams Problems with Solutions Pdf - 1. 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. This is depicted in the diagram below. The resultant velocity of the plane (that is, the result of the wind velocity contributing to the velocity due to the plane's motor) is the vector sum of the velocity of the plane and the velocity of the wind. The resultant velocity of the boat is 5 m/s at 36.9 degrees. You are using an out of date browser. Although the person on the ground might not be moving, according to you they are moving backwards and they have a velocity relative to you. time = (80 m)/ (4 m/s) = 20 s. It requires 20 s for the boat to travel across the river. To determine the resultant velocity, the plane velocity (relative to the air) must be added to the wind velocity. 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. 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. This resultant velocity is quite easily determined if the wind approaches the plane directly from behind. A boat's speed with respect to the water is the same as its speed in still water. b. 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. II. This means that the velocity of the boat with respect to the ground will be: $\begin{align} &v_{B}=\dfrac{2}{0.5} \\ &v_{B}=4 \dfrac{\mathrm{~km}}{ \mathrm{hr}} \end{align}$. III. 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. The speed downstream is 12 kmph. 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 is the hypotenuse of a right triangle with sides of 4 m/s and 7 m/s. This example can be examined under two part vertical and horizontal motion as in the case of projectile motion. What is the resultant velocity of the motor boat? So in order for the boat to go along the shortest path it has to go at an angle of $\theta=\cos^{-1}\left(\dfrac{u}{v}\right)$ with the vertical. 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. Already emphasised before, this difference is not the ordinary difference because velocities are vectors. 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. 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. The boat is carried 60 meters downstream during the 20 seconds it takes to cross the river. The velocity of object A relative to B is represented as vAB. The time to cross this 80-meter wide river can be determined by rearranging and substituting into the average speed equation. Its direction can be determined using a trigonometric function. d. A 60 mi/hr crosswind would increase the resultant velocity of the plane to 100 mi/hr. Since the boat is travelling downstream, this means that the velocity of the boat and the river have the same direction. This is the time taken along the shortest path. A boat has a velocity of 10$\dfrac{km}{hr}$ in still water and it crosses a river of width 2 km. In fact, the current velocity itself has no effect upon the time required for a boat to cross the river. a. 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, $\begin{align} &t=\dfrac{d}{v\left(\dfrac{\sqrt{v^{2}-u^{2}}}{v}\right)} \\ &t=\dfrac{ d}{\sqrt{v^{2}-u^{2}}} \end{align}$. Thus, the Pythagorean theorem can be used to determine the resultant velocity. Furthermore, you can find the "Troubleshooting Login Issues" section which can answer your unresolved problems and equip you with a lot of relevant information. It is. 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. CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. This means that, $\begin{align} &u-v \cos \theta=0 \\ \\ &v \cos \theta=u \\ \\ &\cos \theta=\dfrac{u}{v} \\ \\ &\theta=\cos ^{-1}\left(\dfrac{u}{v}\right) \end{align}$. 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. These two parts (or components) of the motion occur simultaneously for the same time duration (which was 20 seconds in the above problem). 1. A man went downstream for 28 km in a motor boat and immediately returned. Using $v_{B W}=v_{B}-v_{W}$ we can find the value of, River boat problem is a part of relative velocity. To illustrate this principle, consider a plane flying amidst a tailwind. and they are moving relative to some common stationary frame of reference. The distance downstream corresponds to Distance B on the above diagram. 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. $\left|v_{B W}\right|^{2}=\left|v_{B}\right|^{2}+\left|v_{W}\right|^{2}$.(1). And so the average speed of 3 m/s (average speed in the downstream direction) should be substituted into the equation to determine the distance. If a motorboat were to head straight across a river (that is, if the boat were to point its bow straight towards the other side), it would not reach the shore directly across from its starting point. Together, these two parts (or components) add up to give the resulting motion of the boat. To solve any river boat problem, two things are to be kept in mind. The difficulty of the problem is conceptual in nature; the difficulty lies in deciding which numbers to use in the equations. We use cookies to provide you with a great experience and to help our website run effectively. (7.1 m/s @ 32.340 South of East) b. Find the man's rate in still water? We come into situations when one or more objects move in a non-stationary frame with respect to another observer. The shortest path in the river boat problems is when the boat moves perpendicular to the river current. For instance, we observe the plane flying in the air, velocity of that plane . b. 1. 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If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore? It requires 20 s for the boat to travel across the river. This whole situation will become clear with some numerical examples that well see in the next section. 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. Relative Velocity and River Boat Problems. vB = 25 \[ \dfrac{\mathrm{~km}}{ \mathrm{hr}} \]. Q 4. The observed speed of the boat must always be described relative to who the observer is. In all these cases, we must consider the medium's effect on the item to characterise the object's whole motion. Make an attempt to answer the three questions and then click the button to check your answer. In Example 2, the current velocity was much greater - 7 m/s - yet the time to cross the river remained unchanged. In Example 1, the time to cross the 80-meter wide river (when moving 4 m/s) was 20 seconds. This means that: . The solution to the first question has already been shown in the above discussion. 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). A plane can travel with a speed of 80 mi/hr with respect to the air. Even though they have opposite directions, their magnitude remains the same. Example: Velocity of the boat with respect to river is 10 m/s. If the river has a velocity downstream, the actual resultant velocity of the motorboat will not be the same as it was initially. 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The component of motion perpendicular to this direction - the current velocity - only affects the distance that the boat travels down the river. Before starting with the questions, go through the basic concepts of the topic. It is often said that "perpendicular components of motion are independent of each other." $\left|v_{A B}\right|=\left|v_{B A}\right|$. 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. The angle ##\theta## is a parameter and you will obtain different results for different angles. Please define your variables properly. If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore? This question can be answered in the same manner as the previous questions. Since velocity is a vector, the calculations of relative velocity include vector algebra. Here at Smartkeeda, you will get Boat and Streams PDF with Tricks to Solve Fast. (a) Find the path which he should take to reach the point directly opposite to his starting point in the shortest time. Let v denote the velocity vectors and v . The mathematics is easy! As shown in the diagram below, the plane travels with a resulting velocity of 125 km/hr relative to the ground. 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. 2. This angle can be determined using a trigonometric function as shown below. If, is the velocity of the boat with respect to the water, and. The resultant is the hypotenuse of a right triangle with sides of 5 m/s and 2.5 m/s. And the diagonal distance across the river is not known in this case. You are asked to find the shortest time possible so you need to minimise the time as a fuction of the angle. River boat problem is a part of relative velocity. I have the drift of the boat as a function of the angle. It is confusing at first, but is indeed an important topic for. b. 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. 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. Every year at least 1 question is asked from the kinematics part and the probability of relative velocity being asked is quite high due to the variety of questions that can be framed. The resultant velocity of the boat is the vector sum of the boat velocity and the river velocity. The magnitude of the resultant velocity is determined using Pythagorean theorem. (b) Find the time required to reach the destination. 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. a. A tailwind is merely a wind that approaches the plane from behind, thus increasing its resulting velocity. This can be determined using the Pythagorean theorem: SQRT[ (80 mi/hr)2 + (10 mi/hr)2 ] ). Boats & Streams is one of the favorite areas of examiners. In such instances as this, the magnitude of the velocity of the moving object (whether it be a plane or a motorboat) with respect to the observer on land will not be the same as the speedometer reading of the vehicle. If the boat crosses the river along the shortest path possible in 30 minutes, calculate the velocity of the river water. 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. The time to cross the river is dependent upon the velocity at which the boat crosses the river. 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. Now consider a plane traveling with a velocity of 100 km/hr, South that encounters a side wind of 25 km/hr, West. Part c of the problem asks "What distance downstream does the boat reach the opposite shore?" So, they will follow the rules of vector algebra. So we take x to be the drift of the man and then find the time (of course as a function of the angle)? We will start in on the second question. A motorboat traveling 5 m/s, East encounters a current traveling 2.5 m/s, South. River boat problem is similar to other problems like rain man problems or the aeroplane problems. With what average speed is the boat traversing the 80 meter wide river? No! vBW = 15$\dfrac{km}{hr}$, and vW = 10$\dfrac{km}{hr}$. How far he has to walk it will depend on the angle at which he rows. That is, the across-the-river component of displacement adds to the downstream displacement to equal the resulting displacement.
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