Question

a balloon is at a height of 81 m and is ascending upwards with a velocity of 12m/s^2. a body of 2kg weight is dropped from it. if g=10m/s^2, the body will reach the surface of earth in how much time

Answer 1

Since we're observing the vertical motion of the balloon that's ascending, we can use the equation as shown below. 

$d = vt + \frac{1}{2}at^{2}$

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

$81 = 12t + \frac{1}{2}(-10)t^{2}$
$81 = 12t - 5t^{2}$
$-5t^{2} + 12t -81 = 0$

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 can not be negative). 

$t = \frac{-(12) - \sqrt{(12)^{2} - 4(-5)(81)}}{2(-5)}$
$t = 5.4$

This means that it will take 5.4 seconds for the body to reach the ground.

Answer: 5.4 seconds