Answer:



The given problem is related to the motion of a balloon which starts rising from the ground with an upward acceleration of 2 m/s2. After 1 second, a stone is dropped from it and we have to find the time taken by the stone to strike the ground.



To solve the problem, we will use the equations of motion. We will first find the height of the balloon after 1 second and then use the equation of motion to find the time taken by the stone to reach the ground.



Let's assume that the initial velocity of the balloon is zero. Then, the height of the balloon after 1 second can be calculated as follows:

h = 1/2 * a * t^2
where a = 2 m/s2 (upward acceleration)
and t = 1 s (time taken)

h = 1/2 * 2 * 1^2
h = 1 m

Therefore, the height of the balloon after 1 second is 1 meter.

Now, when the stone is dropped from the balloon, it will start falling with an acceleration of 9.8 m/s2 (downward acceleration due to gravity). Let's assume that the time taken by the stone to reach the ground is t1. Then, using the equation of motion, we can write:

h = 1/2 * g * t1^2
where g = 9.8 m/s2 (downward acceleration due to gravity)

Substituting the value of h as 1 meter, we get:

1 = 1/2 * 9.8 * t1^2

Solving for t1, we get:

t1 = sqrt(2/9.8)
t1 = 0.45 s (approx)

Therefore, the time taken by the stone to strike the ground is approximately 0.45 seconds.



In this way, we can solve the given problem using the equations of motion. The key to solving such problems is to identify the correct equations to use and to substitute the given values correctly.

The balloon starts to rise vertically upward with an acceleration of
After one second (First Case)
Therefore in this case;
The distance traveled in this case by the formula
∴ s = 1m
Case Two:-
From there a stone was dropped...
Therefore the stone was falling under the effect of gravity
Therefore in this case;
The time can be calculated in this case by the formula
∴ t ≈ 0.45s