Join now for JEE/NEET and also prepare for Boards Join now for JEE/NEET and also prepare for Boards. Register Now
Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
A river is flowing from west to east at speed of 5 m/minute . A man on south bank of river, capable of swimming at 10 m/min in still water, wants to swim across river in shortest time. He should swim in direction a)due north. b)30 east of north. c) 30 north of west. d) 60 east of north. Justify you answer. A river is flowing from west to east at speed of 5 m/minute . A man on south bank of river, capable of swimming at 10 m/min in still water, wants to swim across river in shortest time. He should swim in direction a)due north. b)30 east of north. c) 30 north of west. d) 60 east of north. Justify you answer.
-------------> V river = 5m/min V man = 10 m/minsuppose width of river is x mts Case 1 if he travels due north then his resultant velocty ( due to velocity of downstream of water) acts 30 north of east and the distane to be covered to reach the other bank increses to = x/cos 30 i.e., 2x /31/2 and resultant velocity is 11.2 m/min so time taken is x / 9.7 mins Case 2 if he travels due 30 north of east then his resultant velocty ( due to velocity of downstream of water) actsdue north and the distane to be covered to reach the other bank will be x mts and resultant velocity is 8.7 m/min so time taken is x / 8.7 mins So case 1 takes least time he should travel due north(a)
-------------> V river = 5m/min
V man = 10 m/minsuppose width of river is x mts
Case 1
if he travels due north
then his resultant velocty ( due to velocity of downstream of water) acts 30 north of east and the distane to be covered to reach the other bank increses to = x/cos 30
i.e., 2x /31/2 and resultant velocity is 11.2 m/min
so time taken is x / 9.7 mins
Case 2
if he travels due 30 north of east
then his resultant velocty ( due to velocity of downstream of water) actsdue north and the distane to be covered to reach the other bank will be x mts and resultant velocity is 8.7 m/min
so time taken is x / 8.7 mins
So case 1 takes least time
he should travel due north(a)
he should swim due north!!! his velocity in moving water is equal to his own velocity plus the velocity of the river. now to cross the river in smallest possible time he should maximise the velocity in the north direction. suppose he move at an angle of @ from the bank then the component due north is 10sin@m/min. because river velocity is zero in the north direction. now this velocity due noth will be maximum when @ tends to 90 degrees. hence he should move due north that is 90 degrees to the bank.
he should swim due north!!!
his velocity in moving water is equal to his own velocity plus the velocity of the river.
now to cross the river in smallest possible time he should maximise the velocity in the north direction.
suppose he move at an angle of @ from the bank then the component due north is 10sin@m/min. because river velocity is zero in the north direction.
now this velocity due noth will be maximum when @ tends to 90 degrees.
hence he should move due north that is 90 degrees to the bank.
Thus ,the resultant of the Velocity of man in still water (Vm)(=OA)and the Velocity of water (Vw)(=OB) is along OP, and is given by (V)(=OC)In right triangle OCA , we haveSin x= AC/OA=Vw/Vm =5/10 = 1/2x=30°Therefore, the man should start swimming at an angle of 30° (west of north)
Yes we should move due north to cover the distance in the shortest time as then the velocity of river and man will get added up and distance would be covered in the shortest time
If the man crossed the river with a angle @ to examined the river velocity then he should travel due north with velocity vcos@.so time taken to cross the river is d/vcos@.after differentiate both the sides of eqn we get @=0. So he should travel in north direction.
hello studentThe given condition can be shown as infigureTime taken to cross the river,t=d/Vscosθfor time to be minimum,cosθ=maximum⇒θ=0So, summer should swim due North.hope it helpsthankyou
hello studentsHope it helpsThankyou
-------------> V river = 5m/min V man = 10 m/minsuppose width of river is x mtsCase 1if he travels due norththen his resultant velocty ( due to velocity of downstream of water) acts 30 north of east and the distane to be covered to reach the other bank increses to = x/cos 30i.e., 2x /31/2 and resultant velocity is 11.2 m/minso time taken is x / 9.7 minsCase 2if he travels due 30 north of eastthen his resultant velocty ( due to velocity of downstream of water) actsdue north and the distane to be covered to reach the other bank will be x mts and resultant velocity is 8.7 m/minso time taken is x / 8.7 minsSo case 1 takes least timeHENCE HE SHOULD TRAVEL TOWARDS NORTH.SO A OPTION IS CORRECT
HENCE HE SHOULD TRAVEL TOWARDS NORTH.
SO A OPTION IS CORRECT
Dear StudentIn order to swim across the river in the shortest time, the man should swim straight due north.Because the velocity of the river is west to east and there is no component in north-south. So, it will not affect the man's time in order to swim to the other bank.I hope this answer will help you.Thanks & RegardsYash Chourasiya
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -