a stone is dropped from arising balloon at a height of 76m above the ground and reaches the ground in 6 seconds. Caculate the velocity of ballon when the stone was dropped?

To calculate the velocity of the balloon when the stone was dropped, we need to use the equation of motion for freely falling objects:

\[ v = u + gt \]

Where:
v = final velocity (which is the velocity of the balloon when the stone was dropped)
u = initial velocity (which is 0 m/s because the balloon is initially at rest)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken for the stone to reach the ground (6 seconds)

Plugging in the values into the equation, we get:

\[ v = 0 + (9.8 \times 6) \]

\[ v = 58.8 \, \text{m/s} \]

Therefore, the velocity of the balloon when the stone was dropped is 58.8 m/s.

To calculate the velocity of the balloon when the stone was dropped, we can use the equations of motion.

The equation that relates the final velocity (vf), initial velocity (vi), acceleration (a), and time (t) is:

vf = vi + a * t

In this case, the final velocity of the balloon when the stone was dropped (vf) is zero because the balloon is just starting to descend, so it has no velocity yet. The acceleration due to gravity (a) is approximately 9.8 m/s², and the time taken for the stone to reach the ground (t) is 6 seconds.

Plugging in these values into the equation, we have:

0 = vi + 9.8 * 6

Rearranging the equation to solve for the initial velocity (vi):

vi = -9.8 * 6

Calculating the result:

vi = -58.8 m/s

Therefore, the velocity of the balloon when the stone was dropped is -58.8 m/s. Note that the negative sign indicates that the velocity is directed downward.