If a boat can go with a maximum velocity of 40 km/hr with respect to water in a pond, then what will be the boat's maximum velocity with respect to water in a river flowing at 20 km/hr.
(i) upstream (ii) downstream respectively.
If a boat can go with a maximum velocity of 40 km/hr with respect to water in a pond, then what will be the boat's maximum velocity with respect to water in a river flowing at 20 km/hr.
(i) upstream (ii) downstream respectively.
The correct option is D 40 km/hr; 40 km/hr
Velocity of boat with respect to water will always be the same, what will change is the velocity of the boat as it will look to a person standing on the ground.
The boat is going with v = 40Km/hr and since water's velocity is 0 it also looks from the ground as going with v = 40
What I mean is,
vbw=40=vbg−vwg
40=vbg−0
Now you see. Okay it will be clearer in river
River - downstream
Intuitively, we know that the motors of the boat can only make it go with 40 km/hr but since the water is pushing too with 20 km it looks like to a person on ground that the boat is going with 60 km. In 1 hr boat was displaced 40 km and water pushed it 20 so to a person on ground boat moved 60 km.
To make it even more simple, lets drop a swimming tube in water at t = 0 why? Hmm...... because a tube doesn't have an engine so it will move with the flow of water.
So with respect to water, the tube will be stationary.
After 1 hr the tube would be displaced by 20 km.
∵That's the speed of water but boat will be displaced by 60 km as its speed was 40km/hr in still water and now it's getting pushed by water with 20 km/hr. Now w.r.t. tube how far has the boat gone?
40 km in 1 hr right?
So the boat's velocity w.r.t. the tube or water is still 40 km/hr.
Down stream
Now the boat is trying its best to go with 40 km/hr in opposite direction but water is pushing it with 20 km/hr in opposite direction. So it ends up going only 20 km upstream as seen by a person on the ground. In the mean time, the tube has also gone 20 km downstream with the river water. So w.r.t. tube, the boat was displaced by 40 km in 1 hr. so boat's velocity w.r.t. water is 40 km/hr.
40 km/hr; 40 km/hr
Velocity of boat with respect to water will always be the same, what will change is the velocity of the boat as it will look to a person standing on the ground.
The boat is going with v = 40Km/hr and since water's velocity is 0 it also looks from the ground as going with v = 40
What I mean is,
vbw=40=vbg−vwg
40=vbg−0
Now you see. Okay it will be clearer in river
River - downstream
Intuitively, we know that the motors of the boat can only make it go with 40 km/hr but since the water is pushing too with 20 km it looks like to a person on ground that the boat is going with 60 km. In 1 hr boat was displaced 40 km and water pushed it 20 so to a person on ground boat moved 60 km.
To make it even more simple, lets drop a swimming tube in water at t = 0 why? Hmm...... because a tube doesn't have an engine so it will move with the flow of water.
So with respect to water, the tube will be stationary.
After 1 hr the tube would be displaced by 20 km.
∵That's the speed of water but boat will be displaced by 60 km as its speed was 40km/hr in still water and now it's getting pushed by water with 20 km/hr. Now w.r.t. tube how far has the boat gone?
40 km in 1 hr right?
So the boat's velocity w.r.t. the tube or water is still 40 km/hr.
Down stream
Now the boat is trying its best to go with 40 km/hr in opposite direction but water is pushing it with 20 km/hr in opposite direction. So it ends up going only 20 km upstream as seen by a person on the ground. In the mean time, the tube has also gone 20 km downstream with the river water. So w.r.t. tube, the boat was displaced by 40 km in 1 hr. so boat's velocity w.r.t. water is 40 km/hr.
