Question

∆ NO USELESS ANSWERS ∆

A boat travels upstream in a river with constant but unknown speed. At start of trip upstream, a bottle is dropped over the side. After 7.5 min the boat turns and head downstream.

It catches up the bottle when the bottle has drifted 1 km downstream from the point at which it was dropped into the water.

What is the velocity of water current ?

∆ Class 11th ∆

Answer 1

Heya.....!!!

Nice question .

This question is based on the concept of Relative Motion .

According to the question , the bottle is dropped over the side , and the boat turns after 7.5 min and then returns to bottle and catch it . In this duration , the bottle has covered 1 Km .

→ Let the speed of bottel be $\bold{u}$ This velocity is same as of water because the bottle is flowing with the speed of water.

When the boat goes and comes back it took total time of. 15 min as it took 7.5 min to go and for coming back it will take 7.5 min *( With respect to bottle )

Total Time = 15 min

and in this duration , the bottle moved 1 Km .

★ Speed of bottle = Speed of water current.

$\bold{u = x/t}$

→ x = 1 Km

→ t = 15 min = 15/60 = 1/4 hr

→ Speed = 4 km/hr

$\huge\boxed{u = 4km/hr}$

_____________________________

Hope It Helps You. ☺

Answer 2

boat travels upstream from B to A and down stream from A to B in 3 hours. If the speed of boat in still water is 9 km/hr. and the speed of current is 3 km/hr the distance between A and B (km) is 


A) 4

  B) 6

C) 8

  D) 12


Correct Answer:

  D) 12


Description for Correct answer

Speed down stream = (9+3)=12 km/hr(9+3)=12 km/hr

Speed upstream = (9−3)=6 km/hr(9−3)=6 km/hr

Suppose distance between A and B is x km.

= x6+x12=3, 2x+x=36x6+x12=3, 2x+x=36

3x = 36

x = 12