Speed of stream = 3 kmph. From above equation, $t$ is minimum when denominator is maximum. 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. Problem: Travelling upstream is travelling against the current so the going upstream the boat travels at $s - 3$ mph. \end{align}. \end{align} What is the speed of the boat in still water? \begin{align} The velocity of a boat in still water is 10 km/hr and the velocity of river water is 5 km/hr. The time taken by the boat $t={d}/{|\vec{v}_b|}={30}/{5}=6\;\mathrm{hr}$. The velocity of river flow is 5 km/hr. &\qquad {(\because \mathrm{PQ}=t|\vec{v}_m|\cos\theta=t|\vec{v}_{m/r}|\cos\alpha).} Write the fundamental equation above for the trip upstream. The speed of a stream is 3 mph. \mathrm{AC}=(v_b+v_r)(1)=v_b+v_r. Let speed in sttil water is x km/hr Substitute expressions for AC, BC, and AB and solve to get flow speed $v_r=3\;\mathrm{km/hr}$. Thus, $10\cos\theta=v_b$ and $10\sin\theta=5$ which gives $\theta=30$ degree. \end{align} Two swimmers leave point A on one bank of the river to reach point B lying right across on the other bank. \begin{align} t&=\frac{\text{width of the river}}{\text{component of man velocity along north}} \nonumber\\ Problem:
the ground. Determine the speed of the stream and that of the boat in still water. Then, speed upstream = (x —3) km/hr. Rejecting negative value, as speed cannot be negative. 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. 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. At what angle to the stream direction must the boat move to minimize drifting? What was the velocity u of f his walking if both swimmers reached the destination simultaneously? A boat travels 10 miles upstream in the same time it takes to travel 16 miles downstream. Speed of the boat downstream = (11 + x) km/hr.
reaches the other bank? The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. &=\frac{d}{|\vec{v}_m|\cos\theta}\nonumber\\ So we need to calculate speed downstream and speed upstream first.
Problem: In 13 hours, it can go 40 km upstream and 55 km down-stream. Get more help from Chegg. \end{align}. Speed of the boat in still water = 11 km/hr. The man can row the boat in still water with a speed of 5 m/s. The raft travels from A to B with a speed $v_r$ for time $(1+t)$ hour i.e., A boat moves relative to water with a velocity 5 km/hr. The speed of the boat in still water is 10 miles per hour.
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. To find the speed of the current, we can substitute 10 for the B in any of our equations. Speed downstreams =(15 + 3)kmph Let $\vec{v}_{b/w}$ makes an angle $\theta$ with $\vec{v}_w=5\; \mathrm{km/hr}\;\hat\imath$. A boat travels 10 miles upstream in the same time it takes to travel 16 miles downstream. Find the flow velocity. The rate of the flow of river is 5 km/hr. I just mentioned here because mostly mistakes in this chapter are of this kind only. 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 stream velocity v, = 2.0 km/hour and the velocity if of each swimmer with respect to water equals 2.5 km/hr. A man can swim with a speed of 4.0 km/h in still water. Distance travelled = (18 x 12/60)km Let the speed of boat in still water be x km/hr & let the speed of stream be y km/hr At what angle to the stream direction must the boat move to minimize drifting? = 3.6km, Rate upstream = (15/3) kmph Solution: The speed of boat in still water ($v_{b/w}=5\;\mathrm{km/hr}$) is less than the flow speed ($v_{b}=10\;\mathrm{km/hr}$). \end{align} According to the given information, 121 - x 2 = 96. x 2 = 25. x = 5. He should swim in a direction?
Given, $|\vec{v}_{m/r}|=10 \,\mathrm{metre/min}$, a constant.
The speed of river water is $v_w$. What is the time taken by the boat if it travels same distance upstream? 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. Thus, time taken to travel a distance $\mathrm{AB}=2.5\; \mathrm{km}$ is $t=\mathrm{AB}/v_b=0.5\;\mathrm{hr}=30\;\mathrm{min}$. Suppose that the speed of the boat in still water is $s$ mph and the time it takes to travel the 10 miles upstream is $t$ hours. Thus, time taken by the boat to travel a distance $d=30\;\mathrm{km}$ is \vec{v}_{m/r}=\vec{v}_m-\vec{v}_r. Problem: (IIT JEE 1988) A boat, which has a speed of 5 km/hr in still water, crosses a river of width 1 km along the shortest possible path in 15 minutes.
\begin{align} Let $d$ be the width of the river. 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. A boat moves relative to water with a velocity 10 km/hr. \text {Speed upstream =}\\ (\frac{15}{3\frac{3}{4}}) km/hr \\ 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). The boat cannot cross the river to an exactly opposite point. \end{align} Find out the speed of the boat in still water. Question: To cross a river in minimum time, your speed relative to the water should be perpendicular to the river flow. speed of current = 1/2(speed downstream - speed upstream) [important] 3. Question from Hannah, a student: The speed of a stream is 3 mph. \mathrm{BC}=(v_b-v_r)t.\nonumber \end{align} \theta=\cos^{-1}-\frac{v_{b/w}}{v_w}=\cos^{-1}-\frac{1}{2}=150\;\mathrm{degree}. \begin{align} The speed of a boat relative to the water is equal to the speed of boat in still water. A boat takes 3 hours to cover a certain distance when going with the stream and 5 hrs to return to the starting point. t=\frac{d}{|\vec{v}_b|}=\frac{30}{15}=2\;\mathrm{hr}\nonumber The velocity of boat relative to the ground is given by relative velocity formula $\vec{v}_b=\vec{v}_{b/w}+\vec{v}_w=15\;\mathrm{km/hr}\:\hat\imath$. \end{align} 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. \vec{v}_{b/w}=\vec{v}_b-\vec{v}_w \nonumber Formula: Speed in still water (km/hr)= (1 / 2) (a + b) Rate of stream (km/hr)= (1 / 2) (a - b) Solution: \end{align} &=\frac{d}{|\vec{v}_{m/r}|\cos\alpha}. = 5 \times \frac{2}{5} = 2 km/hr \\ \\ Problem: (IIT JEE 1983) A river is flowing from west to east at a speed of 5 metre/minute. 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. What is speed at which the boat travels downstream? The boat crosses the river by the shortest path if it moves perpendicular to the river current. The speed of the boat in its return journey (upstream) is $v_b-v_r$. water i.e., 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. \begin{align} The speed of the boat in still water is 15km/hr.It can go 30 km upstream and return to down stream in 41/2hrs.find the speed of the stream. The velocity of the river water is? Now, $\mathrm{AB}=\mathrm{AC}-\mathrm{BC}=6\;\mathrm{km}$. \begin{align} The boat travels for 1 hr downstream with a speed $v_b+v_r$. Hence, the man takes the shortest time when he swims perpendicular to the river velocity i.e., towards north. 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. Solution: The speed of the river current is $v_r=3\;\mathrm{km/hr}$ and speed of the boat relative to the water is $v_{b/r}=7\;\mathrm{km/hr}$. Speed of the boat upstream = (11 - x) km/hr. 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 … v_{b/r}\sin(30+\theta)&=v_r+v_b\sin30 let x=speed of stream (15+x)=speed of boat downstream