Home
Class 12
MATHS
Two roads AB and BC intersect at B, wher...

Two roads AB and BC intersect at B, where `angleABC = 60^(@)` and `bar(AB)` = 28 meter. A cyclist starts from A and moves towaeds B at the rate of 4m/sec and at the same instant another cyclist starts from B and moves along the road BC at the rate of 8 m/sec. find the rate of change of distance between them 3 seconds.

Text Solution

Verified by Experts

The correct Answer is:
`80pi cm^(2)//sec`
Promotional Banner

Topper's Solved these Questions

  • SIGNIFICANCE OF DERIVATIVE AS RATE OF CHANGE

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITVE EXAMINATION|20 Videos

  • SIGNIFICANCE OF DERIVATIVE AS RATE OF CHANGE

    CHHAYA PUBLICATION|Exercise SHORT ANSWER TYPE QUESTIONS|24 Videos

  • SET THEORY

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

  • STRAIGHT LINE IN THREE DIMENSINAL SPACE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination|19 Videos

Similar Questions

Explore conceptually related problems

A cyclist starts from place A and covers a distance of 2400 m to reach the place B. If the maximum possible acceleration of the cyclist is 2m//sec^2 and its maximum retardation is 4 m//sec^2 , what ts the least time the cyclist can undertake the journey from A to B ?

A man is moving away from a tower 41.6 m high at the rate of 2 m/sec. Find the rate at which the angle of elevation of the top of tower is changing, when he is at a distance of 30m from the foot of the tower. Assume that the eye level of the man is 1.6m from the ground.

An any instant of time, two ships A and B are 70 km apart along a line AB which is directed from north to south . A starts moving towards west at 25km*h^(-1) and at the same time B starts moving towards north at 25km*h^(-1) . Find the distance of closest approach between the two ships and the time required for this.

Two cyclists are in motion towards each other along a slightly inclined hill road. The first cyclist starts with a velocity of 5.4 kg /h and attains a downhill acceleration 0.2 m//s^(2) . The second cyclist is under an uphill retardation of 0.2 m/ s^(2) after starting with a velocity of 18 km/h . If the initial distance between them is 130 m , then when would they meet? What would be their velocities at that instant?

Two flagstaffs stand on a horizontal plane. A and B are two points on the line joining their feet and between them. The angles of elevation of the tops of the flagstaffs as seen from A are 30^@ and 60^@ and as seen from B are 60^@ and 45^@ . If AB is 30 m, then the distance between the flagstaffs is

Two particles A and B move from rest along a straight line with constant accelerations f and f' respectively. If A takes m sec. more than that of B and describes n units more than that of B acquiring the same velocity, then

Two houses stand just on the opposite sides of a road of a village. A ladder that stands against the wall of the first house is at a distance of 6 metres from the house and makes an angle of 30^(@) with the horizontal line.But if the ladder stands against the wall of the second house keeping its foot at the same point, it makes an angle of 60^(@) with the horizontal line. (a) Find the length of the ladder. (b) Calculate the distance of the foot of the ladder from the foot of the wall of the second house. (c) Find the width of the road. Find the height where the top of the ladder is fixed against the wall of the second house.

A lift in a mine moves down 24m in 8 mins. If its moves in an uniform rate, let's find at what distance below the surface, it will be after 6 mins. If the lift starts from a height 10 m above the ground, let's find how deep the lift will go from the surface after 70 mins.

A partical is moving along the x-axis. The position of the partical at any instant is given by x = a+ bt^(2) where, a = 6 m and b = 3.5 "m.s"^(-2) ,t is measured in second. Find the average velocity between t = 3s and t = 6 s.

CHHAYA PUBLICATION-SIGNIFICANCE OF DERIVATIVE AS RATE OF CHANGE-LONG ANSWER TYPE QUESTIONS
  1. In the triangle ABC, if the sides a,b reamain constant but the base an...

    Text Solution

    |

  2. The period of oscillation T of a simple pendulum of length l is connec...

    Text Solution

    |

  3. The radius of sphere is found to be 20 cm with a possible error fo 0.0...

    Text Solution

    |

  4. Show that the relative error in computing the volume of cube, due to ...

    Text Solution

    |

  5. The radius of a balloon is 7 cm. If an error of 0.01 cm is made n meas...

    Text Solution

    |

  6. Water is flowing into a right circular conical vessel, 24 inches deep ...

    Text Solution

    |

  7. A man 6 ft tall walks away from the foot of a lamp-post 15 ft high at ...

    Text Solution

    |

  8. A man 6 ft tall walks away from the foot of a lamp-post 15 ft high at ...

    Text Solution

    |

  9. The base of a water tank is a square of side 3 ft. find the rate of fl...

    Text Solution

    |

  10. Sand is poured onto the ground at the rate of 3 ft^(3) /min to form a ...

    Text Solution

    |

  11. A ladder 26 ft long leans against a vertical wall. If the top slides d...

    Text Solution

    |

  12. A balloon leaves the ground 50 ft from an obsever, If it rises vertica...

    Text Solution

    |

  13. A light is placed on the groung at a distance of 30 ft from a house. A...

    Text Solution

    |

  14. A kite is 160 ft high and there are 200 ft of string out. If the wind ...

    Text Solution

    |

  15. Water is pumped out at a constant rate of 88 m^(3)/min from a conical ...

    Text Solution

    |

  16. A circular ink-blot grows at the rate of 2 cm^(2)/s. find the rate at ...

    Text Solution

    |

  17. Two roads AB and BC intersect at B, where angleABC = 60^(@) and bar(AB...

    Text Solution

    |

  18. Find the rate of change of the area of a circle with respect to its ra...

    Text Solution

    |

  19. A stone is dropped into a quiet lake and waves move in circles at a sp...

    Text Solution

    |

  20. An aeroplane is flying horizontally at a height (2)/(3) km above the g...

    Text Solution

    |