Home
Class 11
PHYSICS
A man in a river boat must get from poin...

A man in a river boat must get from point `A` to point `B` on the opposite bank of the river (see figure).The distance `BC=a`.The width of the river `AC=b`.At what minimum speed `u` relative to the still water should the boat travel to reach the point `B`?The velocity of flow of the river is `v_(0)`

A

`(v_(0)b)/(sqrt(a^(2)+b^(2)))`

B

`(v_(0)a)/(sqrt(a^(2)+b^(2)))`

C

`(v_(0)b)/(sqrt(2)a)`

D

`(v_(0)a)/(sqrt(2)b)`

Text Solution

Verified by Experts

The correct Answer is:
a

Suppose u is the speed of the boat relative to water, then velocity of the flow (w.r.t. bank) `v_(0)`.
`v_(x)=(u cos theta+v_(0))`, and perpendicu lar to flow will be `u_(y)=u sin theta`
Time to cross the river, `t=(b)/(u sin theta)` In the time, the distance travelled by the boat in the direction of flow.
`a=v_(x)t=(u cos theta+v_(0))(b)/(u sin theta)`
or `au sin theta=ub cos theta+v_(0)b`

`therefore u=(v_(0)b)/((alpha sin theta-b cos theta))`.............(i) u to be minimum.
`theta=0` or `(d)/(dtheta)[(v_(0)b)/(alpha sin theta-b cos theta)]=0`
or `tan theta=-(a)/(b) therefore cos theta=(b)/(sqrt(a^(2)+b^(2))`
On substituting these values in equation (i), we get
`u_("min")=(v_(0)b)/(sqrt(a^(2)+b^(2))`
Promotional Banner

Topper's Solved these Questions

  • MOTION IN A STRAIGHT LINE

    GRB PUBLICATION|Exercise Comprehension type Queston|14 Videos
  • UNITS AND DIMENSIONS

    GRB PUBLICATION|Exercise Link Compression|6 Videos

Similar Questions

Explore conceptually related problems

A man in a row boat must get from point A to point B on the opposite bank of the river (see figure).The distance BC=a .The width of the river AC=b .At what minimum speed u relative to the still water should the boat travel to reach the point B ?The velocity of flow of the river is v_(0)

A man wants to reach point B on the opposite bank of a river flowing at a speed 4m//s as shown in the figure. What minimum speed relative to water should the man have so that he can reach point B directly by swimming?

A man wants to reach point B on the opposite bank of a river flowing at a speed u as shown in (Fig. 5.193). What minimum speed relative to water to water should the man have so that he can reach directly to point B ? In which direction should he swim ? .

A man wants to reach point B on the opposite bank of a river flowing at a speed as shown in figure. What minimum speed relative to water should the man have so that he can reach point B? In which direction should he swim?

A man wants to reach point B on the opposite bank of a river flowing at a speed 4m/s as shown in the fig 1E.125 (a) what minimum speed relative to water should the man have so that he can reach point B directly by swimming? In which direction should he swin?

A man who can swim at a speed v relative to the water wants to cross a river of width d flowing with a speed u. The point opposite him across the river is A.

GRB PUBLICATION-MOTION IN TWO AND THREE DIMENSIONS-All Questions
  1. A man wishes to cross a river flowing with velocity u swims at an angl...

    Text Solution

    |

  2. Consider a collection of a large number of particles each with speed v...

    Text Solution

    |

  3. A man in a river boat must get from point A to point B on the opposite...

    Text Solution

    |

  4. A motor boat has a speed of 5 m//s.At time t=0,its position vector rel...

    Text Solution

    |

  5. A 400 m wide river is flowing at a rate of 2.0 m s^-1. A boat is saili...

    Text Solution

    |

  6. Figure shows a sphere moving in a steady flow of air in the x-directio...

    Text Solution

    |

  7. A particle is projected from an inclined plane OP1 from A with velocit...

    Text Solution

    |

  8. A particle is dropped from point P at time t = 0. At the same time an...

    Text Solution

    |

  9. Shots are fired simu ltaneou ly from the top and bottom of a vertical ...

    Text Solution

    |

  10. In the figure shown, the two projectile are fired simultaneously. Find...

    Text Solution

    |

  11. An open merry go round rotates at an angular velocity omega.A person s...

    Text Solution

    |

  12. A person standing on a road has to hold his umbrella at 60^(0) with th...

    Text Solution

    |

  13. From a point A on bank of a channel with still water a person must get...

    Text Solution

    |

  14. A fighter plane enters inside the enemy territory, at time t=0, with v...

    Text Solution

    |

  15. A bomber plane moving at a horizontal speed of 20 m//s releases a bomb...

    Text Solution

    |

  16. A particle P is projected from a point on the surface of smooth inclin...

    Text Solution

    |

  17. A particle is projected from surface of the inclined plane with speed ...

    Text Solution

    |

  18. A smooth square plateform ABCD is moving towards right with a uniform ...

    Text Solution

    |

  19. A shell is projected from a gun with a muzzle velocity u.The gun is fi...

    Text Solution

    |

  20. In case of projectle motion if two projectles A and B are projected wi...

    Text Solution

    |