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A balloon starts raising from the ground with an acceleration of 1.25m/s2. After 8 seconds , a stone is released from the balloon. The stone will (g=10m/s2), a) reach the ground in 4s b) begin to move down after being released c) have a displacement of 50m d) covers a distance of 40m in reaching the ground. Correct answer is option 'a'. Explain the answer.?
Most Upvoted Answer
A balloon starts raising from the ground with an acceleration of 1.25m...
Initial velocity, u = 0m/s
acceleration, a =1.25 m/s^2
Velocity of balloon after 8 s, v = u +at
=> v = 0 + 1.25 x 8 = 10m/s
Displacement of balloon in 8 s,
s=ut+1/2at^2
= 0+1/2 x 1.25 x 8^2
= 40m
After t = 8s, a stone is dropped.
Initial velocity of stone at time of fall is same as that of balloon at that time :
That is velocity of stone,when it is dropped is 10m/s upward.
Initial velocity, u = 10m/s
Displacement, s = -40m ( - means downward)
Balloon is left.
Acceleration, a = -10 m/s^2
So, time taken by stone to reach
s = ut + 1/2 at^2
-40 = 10t + 1/2 x (-10) x t^2
t^2 - 2t - 8 = 0
(t + 2)(t-4) = 0
t = 4 s, t = -2
Stone wil take 4s to reach the ground.
Hope It Helps!!
Community Answer
A balloon starts raising from the ground with an acceleration of 1.25m...
Given information:
- Balloon's acceleration = 1.25 m/s²
- Time = 8 seconds
- Stone is released after 8 seconds.
To find:
- What will happen to the stone?
Solution:
1. Balloon's motion:
The balloon is rising from the ground with an acceleration of 1.25 m/s². This means that its velocity is increasing by 1.25 m/s every second. After 8 seconds, the velocity of the balloon is given by:
v = u + at
where
v = final velocity of the balloon
u = initial velocity of the balloon (since the balloon starts from rest, u = 0)
a = acceleration of the balloon
t = time (8 seconds)
Substituting the given values:
v = 0 + 1.25 * 8
v = 10 m/s
2. Stone's motion:
The stone is released from the balloon after 8 seconds. At this point, the stone will have the same velocity as the balloon, which is 10 m/s upwards.
3. Stone's motion after release:
Once the stone is released, it will start moving under the influence of gravity (acceleration due to gravity, g = 10 m/s²). The stone will experience a downward acceleration of 10 m/s² due to gravity.
Since the stone is moving upwards initially with a velocity of 10 m/s, the acceleration due to gravity will cause its velocity to decrease. Eventually, the stone will come to rest and start moving downwards.
4. Time taken to reach the ground:
The stone will reach the ground when its displacement is zero. We can use the equation of motion to find the time taken for this.
v² = u² + 2as
where
v = final velocity of the stone (0 m/s when it reaches the ground)
u = initial velocity of the stone (10 m/s upwards)
a = acceleration due to gravity (-10 m/s²)
s = displacement (unknown)
Substituting the given values:
0² = 10² + 2 * (-10) * s
0 = 100 - 20s
20s = 100
s = 5 meters
This means that the stone will fall a distance of 5 meters before reaching the ground.
5. Conclusion:
The correct answer is option 'a' - the stone will reach the ground in 4 seconds.
- Balloon's acceleration = 1.25 m/s²
- Time = 8 seconds
- Stone is released after 8 seconds.
To find:
- What will happen to the stone?
Solution:
1. Balloon's motion:
The balloon is rising from the ground with an acceleration of 1.25 m/s². This means that its velocity is increasing by 1.25 m/s every second. After 8 seconds, the velocity of the balloon is given by:
v = u + at
where
v = final velocity of the balloon
u = initial velocity of the balloon (since the balloon starts from rest, u = 0)
a = acceleration of the balloon
t = time (8 seconds)
Substituting the given values:
v = 0 + 1.25 * 8
v = 10 m/s
2. Stone's motion:
The stone is released from the balloon after 8 seconds. At this point, the stone will have the same velocity as the balloon, which is 10 m/s upwards.
3. Stone's motion after release:
Once the stone is released, it will start moving under the influence of gravity (acceleration due to gravity, g = 10 m/s²). The stone will experience a downward acceleration of 10 m/s² due to gravity.
Since the stone is moving upwards initially with a velocity of 10 m/s, the acceleration due to gravity will cause its velocity to decrease. Eventually, the stone will come to rest and start moving downwards.
4. Time taken to reach the ground:
The stone will reach the ground when its displacement is zero. We can use the equation of motion to find the time taken for this.
v² = u² + 2as
where
v = final velocity of the stone (0 m/s when it reaches the ground)
u = initial velocity of the stone (10 m/s upwards)
a = acceleration due to gravity (-10 m/s²)
s = displacement (unknown)
Substituting the given values:
0² = 10² + 2 * (-10) * s
0 = 100 - 20s
20s = 100
s = 5 meters
This means that the stone will fall a distance of 5 meters before reaching the ground.
5. Conclusion:
The correct answer is option 'a' - the stone will reach the ground in 4 seconds.
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A balloon starts raising from the ground with an acceleration of 1.25m/s2. After 8 seconds , a stone is released from the balloon. The stone will (g=10m/s2), a) reach the ground in 4s b) begin to move down after being released c) have a displacement of 50m d) covers a distance of 40m in reaching the ground. Correct answer is option 'a'. Explain the answer.?
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A balloon starts raising from the ground with an acceleration of 1.25m/s2. After 8 seconds , a stone is released from the balloon. The stone will (g=10m/s2), a) reach the ground in 4s b) begin to move down after being released c) have a displacement of 50m d) covers a distance of 40m in reaching the ground. Correct answer is option 'a'. Explain the answer.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A balloon starts raising from the ground with an acceleration of 1.25m/s2. After 8 seconds , a stone is released from the balloon. The stone will (g=10m/s2), a) reach the ground in 4s b) begin to move down after being released c) have a displacement of 50m d) covers a distance of 40m in reaching the ground. Correct answer is option 'a'. Explain the answer.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A balloon starts raising from the ground with an acceleration of 1.25m/s2. After 8 seconds , a stone is released from the balloon. The stone will (g=10m/s2), a) reach the ground in 4s b) begin to move down after being released c) have a displacement of 50m d) covers a distance of 40m in reaching the ground. Correct answer is option 'a'. Explain the answer.?.
A balloon starts raising from the ground with an acceleration of 1.25m/s2. After 8 seconds , a stone is released from the balloon. The stone will (g=10m/s2), a) reach the ground in 4s b) begin to move down after being released c) have a displacement of 50m d) covers a distance of 40m in reaching the ground. Correct answer is option 'a'. Explain the answer.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A balloon starts raising from the ground with an acceleration of 1.25m/s2. After 8 seconds , a stone is released from the balloon. The stone will (g=10m/s2), a) reach the ground in 4s b) begin to move down after being released c) have a displacement of 50m d) covers a distance of 40m in reaching the ground. Correct answer is option 'a'. Explain the answer.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A balloon starts raising from the ground with an acceleration of 1.25m/s2. After 8 seconds , a stone is released from the balloon. The stone will (g=10m/s2), a) reach the ground in 4s b) begin to move down after being released c) have a displacement of 50m d) covers a distance of 40m in reaching the ground. Correct answer is option 'a'. Explain the answer.?.
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