Now, $\mathrm{AB}=\mathrm{AC}-\mathrm{BC}=6\;\mathrm{km}$. The velocity of the river water is? Problem: But with the help of speed of boat in still water formula in this page speed in still water and rate of a stream can be calculated on your own based on the speed in upstream and downstream. A man can swim with a speed of 4.0 km/h in still water. In this case, the drift is minimum if $\vec{v}_{b}=\vec{v}_{b/w}+\vec{v}_w$ is perpendicular to $\vec{v}_{b/w}$. Speed downstream = (16 + 5) = 21 kmph Problem: A boat travels 10 miles upstream in the same time it takes to travel 16 miles downstream. One of them crosses the river along the straight line AB 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. The velocity of the man in still water is equal to the relative velocity of the man w.r.t.

Problem: \end{align} The time taken by the boat $t={d}/{|\vec{v}_b|}={30}/{5}=6\;\mathrm{hr}$.

A boat moves relative to water with a velocity 5 km/hr. The velocity of river flow is 10 km/hr. Formula: Speed in still water (km/hr)= (1 / 2) (a + b) Rate of stream (km/hr)= (1 / 2) (a - b) Distance travelled = (18 x 12/60)km Example 19 A boat goes 30 km upstream and 44 km downstream in 10 hours. Let $\vec{v}_{m/r}$ and $\vec{v}_{m}$ make angle $\alpha$ and $\theta$ with the north direction. Speed of stream = 3 kmph. Two swimmers leave point A on one bank of the river to reach point B lying right across on the other bank. \vec{v}_{b/w}=\vec{v}_b-\vec{v}_w \nonumber Because if we neglect it we will not reach on right answer. \theta=\cos^{-1}-\frac{v_{b/w}}{v_w}=\cos^{-1}-\frac{1}{2}=150\;\mathrm{degree}. Find out the speed of the boat in still water. The relative velocity formula gives $\vec{v}_b=\vec{v}_{b/w}+\vec{v}_w$. Let $\vec{v}_{b/r}$ makes an angle $\theta$ with AB.
\begin{align} \nonumber Problem: A boat must get from point A to point B on the opposite bank of the river moving along a straight line AB that makes 120 degree angle with the flow direction. So, x = 5. In 13 hours, it can go 40 km upstream and 55 km down-stream. The distances BC and AC are equal. At what angle to the stream direction must the boat move to minimize drifting? the ground. \text {Speed upstream =}\\ (\frac{15}{3\frac{3}{4}}) km/hr \\ = 15 \times \frac{4}{15} = 4 km/hr \\ Speed of the boat upstream = (11 - x) km/hr. If the river is flowing at 2 m/s, determine the speed of the boat and the angle 0 he must direct the boat so that it travels from A to B. Find the flow velocity. Time = distance/speed = 84/21 = 4 hours, Get Free Current Affairs and Govt Jobs Alerts in your mailbox, Computer Awareness Questions Answers - Set 1, Computer Awareness Questions Answers - Set 2, Important Abbreviations Computer Awareness Questions Answers, Important File Extensions Questions Answers, Computer System Architecture Questions Answers, Read more from - Boats and Streams Questions Answers. Speed of stream (1/2)(7 - 5)kmph = 1 kmph, \begin{aligned}\text{Speed Upstream} = \frac{3}{\frac{20}{60}} = 9 km/hr \\\text{Speed Downstream} = \frac{3}{\frac{18}{60}} = 10 km/hr \\\text{Rate of current will be} \\\frac{10-9}{2} = \frac{1}{2} km/hr\end{aligned}, First of all, we know that Thus, $t$ become minimum when $\cos\alpha =1$ i.e., $\alpha=0$. Lets see the question now. \end{align}. Rate downstream (21/3) kmph = 7 kmph. Speed of the boat in still water = 11 km/hr.

The velocity of river flow is 5 km/hr. The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. What was the velocity u of f his walking if both swimmers reached the destination simultaneously? Let $d$ be the width of the river. The speed of the boat in still water is 10 miles per hour. The velocity of boat relative to the ground is given by relative velocity formula $\vec{v}_b=\vec{v}_{b/w}+\vec{v}_w=15\;\mathrm{km/hr}\:\hat\imath$. He should swim in a direction? If distance AB is 2.5 km, the speed of boat in still water is 7 km/hr and the speed of the river current is 3 km/hr, then the minimum travel time of the boat is? \end{align} The speed of river water is $v_w$. Question: To cross a river in minimum time, your speed relative to the water should be perpendicular to the river flow. Determine the speed of the stream and that of the boat in still water. Rejecting negative value, as speed cannot be negative.
\begin{align} How long does he take to \begin{align} Thus, time taken to travel a distance $\mathrm{AB}=2.5\; \mathrm{km}$ is $t=\mathrm{AB}/v_b=0.5\;\mathrm{hr}=30\;\mathrm{min}$. In upstream motion, the speed of the boat is equal to the difference of the speed of boat in still water and the speed of river water. I just mentioned here because mostly mistakes in this chapter are of this kind only. &=\frac{d}{|\vec{v}_m|\cos\theta}\nonumber\\ \end{align} The raft travels from A to B with a speed $v_r$ for time $(1+t)$ hour i.e.,

A boat takes 3 hours to cover a certain distance when going with the stream and 5 hrs to return to the starting point. Speed = Distance / Time [important] How far down the river does he go when he The time downstream is the same as the stream upstream so now write the fundamental equation for the trip downstream.

The speed of a boat relative to the water is equal to the speed of boat in still water. 4. x-3 = 10 or x = 13 kmph, It is very important to check, if the boat speed given is in still water or with water or against water. = 5 \times \frac{2}{5} = 2 km/hr \\ \text{Speed Downstream = } What is the minimum speed of the boat relative to the water? The velocity of the boat relative to the water is $\vec{v}_{b/w}$ and it makes an angle $\alpha$ to a line perpendicular to $\vec{v}_w$. Given, $|\vec{v}_{m/r}|=10 \,\mathrm{metre/min}$, a constant. What is the speed of the boat in still water? \begin{align} From above equation, $t$ is minimum when denominator is maximum.

The speed of a boat in still water is v. The boat is to make a round-trip in a river whose current travels at speed u.

Question from Hannah, a student: The speed of a stream is 3 mph. \end{align} \mathrm{AC}=(v_b+v_r)(1)=v_b+v_r. \begin{aligned} Exercise: Exercise:

Find the flow velocity. Solution: The speed of the river current is $v_r=3\;\mathrm{km/hr}$ and speed of the boat relative to the water is $v_{b/r}=7\;\mathrm{km/hr}$. If it travels on a river 6 miles downstream in the same amount of time it takes to travel 3 miles upstream, what is the speed of th. Solution: Given, $\vec{v}_w=5\;\mathrm{km/hr}\;\hat\imath$ and $\vec{v}_{b/w}=10\;\mathrm{km/hr}\;\hat\imath$. \end{align}. Solution: The speed of the raft is same as speed of the flow, say $v_r$. Write the fundamental equation above for the trip upstream. Thus, time taken by the boat to travel a distance $d=30\;\mathrm{km}$ is \begin{align} &\qquad {(\because \mathrm{PQ}=t|\vec{v}_m|\cos\theta=t|\vec{v}_{m/r}|\cos\alpha).} Get more help from Chegg. \end{align}

So we need to calculate speed downstream and speed upstream first. To do so, the velocity of boat relative to the ground ($\vec{v}_b$) should be perpendicular to the flow velocity ($\vec{v}_w$). Exercise: A boat must get from point A to point B on the opposite bank of the river. reaches the other bank? Derive a formula for the time needed to make a round trip of total distance D if the boat makes the round-trip by moving a) upstream and … Thus, $10\cos\theta=v_b$ and $10\sin\theta=5$ which gives $\theta=30$ degree. \begin{align} The boat cannot cross the river to an exactly opposite point. Speed of boat in still water from speed of stream and times taken Last Updated: 13-11-2018 Write a program to determine speed of the boat in still water(B) given the speed of the stream(S in km/hr), the time taken (for same point) by the boat upstream(T1 in hr) and downstream(T2 in hr). \begin{align} \begin{align} Solution: Solution: The speed of boat in still water ($v_{b/w}=5\;\mathrm{km/hr}$) is less than the flow speed ($v_{b}=10\;\mathrm{km/hr}$). v_{b/r}\cos(30+\theta)&=v_b\cos30\\ Let $\vec{v}_{b/w}$ makes an angle $\theta$ with $\vec{v}_w=5\; \mathrm{km/hr}\;\hat\imath$. The distance travelled downstream in 12 minutes is. = 3.6km, Rate upstream = (15/3) kmph The stream velocity v, = 2.0 km/hour and the velocity if of each swimmer with respect to water equals 2.5 km/hr. cross a river 1.0 km wide if the river flows steadily at 3.0 km/h and he makes his strokes normal to the river current? The distance traveled by the boat in its downstream journey from A to its turning point C is Problem: A motorboat going downstream overcame a raft at a point A; one hour later it turned back and after some time passed the raft at a distance 6.0 km from the point A. Let $v_b$ be speed of the boat in still water. The speed of a stream is 3 mph. Substitute values, square and add to get t=\frac{d}{|\vec{v}_b|}=\frac{30}{15}=2\;\mathrm{hr}\nonumber Hence, the man takes the shortest time when he swims perpendicular to the river velocity i.e., towards north. Substitute expressions for AC, BC, and AB and solve to get flow speed $v_r=3\;\mathrm{km/hr}$. &=\frac{d}{|\vec{v}_{m/r}|\cos\alpha}. speed of current = 1/2(speed downstream - speed upstream) [important]

Solve one of the equations for $t$ and substitute into the second equations.

We'll choose … \end{align} The angle made by $\vec{v}_{b/w}$ with $\vec{v}_w$ is given by Speed downstreams =(15 + 3)kmph Find the difference between the speed of the boat in still water and that of the current. At what angle to the stream direction must the boat move to minimize drifting? Problem: The velocity of a boat in still water is 10 km/hr and the velocity of river water is 5 km/hr. Question: You cannot cross a river to an exactly opposite point if your speed in still water is less than the speed of river water. A boat moves relative to water with a velocity 10 km/hr. = 1 km/hr \begin{align}

Let the speed of the stream = x km/hr. (\frac{5}{2\frac{1}{2}}) km/hr \\ In this case, $\vec{v}_w=5\;\mathrm{km/hr}\;\hat\imath$, $\vec{v}_{b/w}=-10\;\mathrm{km/hr}\;\hat\imath$, and $\vec{v}_b=\vec{v}_{b/w}+\vec{v}_w=-5\;\mathrm{km/hr}\:\hat\imath$. Solution: Let speed in sttil water is x km/hr = 18 kmph. \begin{align} Then, speed upstream = (x —3) km/hr. According to the given information, 121 - x 2 = 96. x 2 = 25. x = 5. The rate of the flow of river is 5 km/hr. \end{align} The boat crosses the river by the shortest path if it moves perpendicular to the river current. The boat travels for 1 hr downstream with a speed $v_b+v_r$. \vec{v}_{m/r}=\vec{v}_m-\vec{v}_r.

What is the angle made by the velocity of the boat relative to the ground $\vec{v}_b$ with the line perpendicular to $\vec{v}_w$? To solve river boat problems, we need to understand two concepts: Problem: If the boat takes time $t$ hour from C to B then the distance BC is