A balloon is at a height of 81 M and is ascending upwards with a velocity of 12m/s. A body of 2 kg weight is dropped from it. If g= 10m/s^2. The body will reach the surface of the earth in how much time?
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Since we're observing the vertical motion of the balloon that's ascending, for that we can use the equation as shown below.
d = vt + 1/2 at²
where d is the height, v is the velocity, a is the acceleration, and t is the time.
Given that the balloon reached a height of 81 m at a velocity of 12 m/s².
Since a body is dropped and is going downwards, acceleration is equal to g = 10 m/s². So, plugging this into the equation, we have
81 = 12t + 1/2 (-10) t²
81 = 12t - 5t²
- 5t² + 12t - 81 = 0
Seeing that we have a quadratic equation, we can apply the quadratic formula to look for its positive root (we neglect the negative root since time cannot be negative).
t = -(12)- √(12)³ - 4 (-5) (81)/ 2 (-5)
t = 5.4
This means that it will take 5.4 seconds for the body to reach the ground.
Answer: 5.4 seconds
d = vt + 1/2 at²
where d is the height, v is the velocity, a is the acceleration, and t is the time.
Given that the balloon reached a height of 81 m at a velocity of 12 m/s².
Since a body is dropped and is going downwards, acceleration is equal to g = 10 m/s². So, plugging this into the equation, we have
81 = 12t + 1/2 (-10) t²
81 = 12t - 5t²
- 5t² + 12t - 81 = 0
Seeing that we have a quadratic equation, we can apply the quadratic formula to look for its positive root (we neglect the negative root since time cannot be negative).
t = -(12)- √(12)³ - 4 (-5) (81)/ 2 (-5)
t = 5.4
This means that it will take 5.4 seconds for the body to reach the ground.
Answer: 5.4 seconds
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The correct answer is 5.4 seconds.
Thanks.
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