Physics, asked by Devansy1362, 2 days ago

A swimmer can swim in still water with speed 5 km/hr. What is the ratio of time taken by him to swim across a river in shortest time to that over shortest distance? River is flowing with speed 3 km/hr.
Answer:

Answers

Answered by jadhavjitender22
0

Answer:

aap Samar cancel in silver water with speed 5 p.m. what is the time taken by him to same over of living in short take time to that over take this terms is for which century came here answering 5 year 3

Answered by hotelcalifornia
0

Given:

Speed of the river =3km/h

Speed of the swimmer =5km/h

To find:

The ratio of time taken by the swimmer to cross a river in the shortest time to that in the shortest distance.

Solution:

Step 1

If we consider the diagram for the journey for the shortest travelling time.

Let O be the starting point from which the swimmer should start swimming towards B in order to cross the river in the shortest time.

But, due to the flow of the river, the swimmer reaches point P when, OP will  take the shortest time to cross the river.

In ΔBOP, we have,

The vector for the speed of the river BP=3km/h

and, the vector for the speed of the swimmer OP=5km/h

We know,

Speed is the distance traveled by an object in a given time period.

s=\frac{d}{t}

t=\frac{d}{s}

We have,

The time taken to cross the river in shortest time as T_{1} and the distance d=OP with a speed of s=5km/h

T_{1} =\frac{d}{5}          (i)

Step 2

If we consider the diagram of the journey for minimum travelling distance.

Let, A be starting point from where the swimmer should start swimming in order to reach P, which is the shortest distance.

But due to the flow of river, there is a high probability that the swimmer might lose the point P.

Hence, he needs to swim apparently in the diagonally further distance AB In order to reach P.

Now,

In ΔPAB, using Pythagoras theorem, we get

AB^{2}= AP^{2}+ BP^{2}

We have,

The vector for thee speed of the river BP=3km/h and the vector for the speed of the swimmer AB=5km/h

(5)^{2}= AP^{2} +(3)^{2}

AP^{2} ={25-9}

AP=\sqrt{16}

AP=4

Hence, the swimmer need to swim with a speed of 4 km/h in the AB direction in the running river in order to reach P from where, AP is the shortest distance possible to cross the river.

We know,

t=\frac{d}{s}

We have, the time taken by the swimmer to travel apparently AP as T_{2} the distance d=AP with a speed of 4km/h.

T_{2}=\frac{d}{4}            (ii)

Step 3

Now, the ratio of time taken by the swimmer to cross the river in the shortest time to that the shortest distance will be,

\frac{T_{1} }{T_{2} } =\frac{\frac{d}{4} }{\frac{d}{5} }

\frac{T_{1} }{T_{2} }=\frac{5}{4}

Final answer:

Hence, the ratio of time taken by the swimmer to cross the river in the shortest time to the shortest distance is 5 :4.

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