Home
Class 11
PHYSICS
balloon is rising vertically up with a v...

balloon is rising vertically up with a velocity of 29 m/s. A stone is dropped from it and it reaches the ground in 10 seconds. The height of the balloon when the stone was dropped from it is `(g = 9.8 m/s^2)`

A

100m

B

200m

C

400m

D

150m

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the height of the balloon when the stone was dropped from it. We will use the second equation of motion to do this. ### Step-by-Step Solution: 1. **Identify the Given Data:** - Initial velocity of the stone (u) = 29 m/s (upward, same as the balloon's velocity) - Time taken to reach the ground (t) = 10 s - Acceleration due to gravity (g) = 9.8 m/s² (downward, so we will take it as -9.8 m/s²) 2. **Use the Second Equation of Motion:** The second equation of motion is given by: \[ h = ut + \frac{1}{2} a t^2 \] Here, \(a\) is the acceleration, which will be -g (since it acts downward). 3. **Substituting the Values:** - Substitute \(u = 29\) m/s, \(t = 10\) s, and \(a = -9.8\) m/s² into the equation: \[ h = (29 \, \text{m/s}) \times (10 \, \text{s}) + \frac{1}{2} \times (-9.8 \, \text{m/s}^2) \times (10 \, \text{s})^2 \] 4. **Calculating Each Term:** - First term: \(29 \times 10 = 290\) m - Second term: \[ \frac{1}{2} \times (-9.8) \times 100 = -490 \, \text{m} \] 5. **Combining the Results:** \[ h = 290 - 490 = -200 \, \text{m} \] 6. **Interpreting the Result:** Since we are looking for height, we take the absolute value: \[ h = 200 \, \text{m} \] ### Final Answer: The height of the balloon when the stone was dropped from it is **200 meters**.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MOTION IN ONE DIMENSION

    ERRORLESS |Exercise Critical Thinking|19 Videos
  • MOTION IN ONE DIMENSION

    ERRORLESS |Exercise Graphical Questions|23 Videos
  • MOTION IN ONE DIMENSION

    ERRORLESS |Exercise Relative Motion|13 Videos
  • GRAVITATION

    ERRORLESS |Exercise SET|27 Videos
  • MOTION IN TWO DIMENSION

    ERRORLESS |Exercise Exercise|319 Videos

Similar Questions

Explore conceptually related problems

A stone is dropped from a balloon rising upwards with a velocity of 16 ms^(-1) . The stone reaches the ground in 4 s. Calculate the height of the balloon when the stone was dropped.

A stone is dropped from a ballon rising upwards with a velocity of 16 ms ^(-1) . The stone reached the ground in 4s. Calculate the height of the ballon when the stone was dropped.

Knowledge Check

  • A stone is dropped from a bridge and it reaches the ground in 4 seconds. The height of the bridge is

    A
    `78.4` m
    B
    `64` m
    C
    `260` m
    D
    `2000` m
  • From a balloon, ascending with a velocity of 981 cm/sec., a stone is let fall and reaches the ground in 10 seconds. The height of balloon when the stone was dropped was

    A
    392.4 m
    B
    400 m
    C
    450 m
    D
    None of these
  • A stone dropped from the top of a tower reaches the ground in 3 s. The height of the tower is

    A
    18.6 m
    B
    39.2 m
    C
    44.1 m
    D
    98 m
  • Similar Questions

    Explore conceptually related problems

    A stone is dropped from a rising balloon at a height of 76 m above the ground and reaches the ground in 6s. What was the velocity of the balloon when the stone was dropped?

    A stone is dropped from the roof of a building takes 4s to reach ground. The height of the building is

    A ballon is moving vertically up with a velocity 4 m/s. When it is at a height h , a body is gently released from it. If it reaches ground in 4 sec, the height of balloon, when the body is released, is: (Take g = 9.8 m//s^(2) )

    A stone dropped from a building takes 4 s to reach the ground. The height of the building is

    A balloon is moving upwards with velocity 10m//s . It releases a stone which comes down to the ground in 11s . The height of the balloon from the ground at the moment when the stone was dropped is (g=10m//s^(2))