A balloon is ascending at the rate of 12 m/s and is 30.4 meters above the ground. A stone is dropped from the balloon. Determine how much time it will take for the stone to reach the ground.


To solve this problem, we need to use the kinematic equations of motion. We can assume that the initial velocity of the stone is zero since it is being dropped from the balloon. We also know that the acceleration due to gravity is 9.8 m/s^2.


Let's use the following kinematic equation to solve the problem:


h = ut + (1/2)at^2

where h is the height, u is the initial velocity, a is the acceleration, and t is the time.


We can use this equation to find the time it takes for the stone to reach the ground. We know that the initial height of the stone is 30.4 meters and the final height is 0 meters (since it reaches the ground). We also know that the acceleration due to gravity is -9.8 m/s^2 (since it is acting downwards).


Substituting the values in the equation, we get:

0 = 0*t + (1/2)*(-9.8)*t^2 + 30.4

Simplifying, we get:

4.9t^2 = 30.4

t^2 = 6.204

t = 2.49 seconds (rounded off to two decimal places)


Therefore, it will take approximately 2.49 seconds for the stone to reach the ground.


In conclusion, we can find the time it takes for the stone to reach the ground by using the kinematic equations of motion. We can assume that the initial velocity of the stone is zero and the acceleration due to gravity is -9.8 m/s^2. Substituting these values in the equation, we can calculate the time it takes for the stone to reach the ground, which is approximately 2.49 seconds.

3.71 sec by using formula

S = ut + 1/2at^2