The balloon starts rising from rest, which means its initial velocity is zero (u = 0). The upward acceleration of the balloon is given as 2 m/s².



Using the second equation of motion, we can find the velocity of the balloon after 1 second:

v = u + at

where:
v = final velocity of the balloon
u = initial velocity of the balloon
a = acceleration of the balloon
t = time

Plugging in the values, we have:

v = 0 + 2(1)
v = 2 m/s

Therefore, the velocity of the balloon after 1 second is 2 m/s.



When the stone is dropped from the balloon, it starts falling freely under the influence of gravity. The stone experiences a constant acceleration due to gravity, which is approximately 9.8 m/s² (g = 9.8 m/s²).



To calculate the time taken by the stone to strike the ground, we can use the equation of motion for vertical motion:

s = ut + (1/2)at²

where:
s = distance traveled by the stone (which is the height of the balloon)
u = initial velocity of the stone (which is the velocity of the balloon)
a = acceleration of the stone (which is the acceleration due to gravity)
t = time taken by the stone to strike the ground

We need to find the height of the balloon, which is equal to the distance traveled by the stone. Since the stone is dropped from the balloon, the initial velocity of the stone is the same as the velocity of the balloon (2 m/s).

s = 2(1) + (1/2)(9.8)(t²)

s = 2 + 4.9t²

Now, we need to find the time taken by the stone to reach the ground. At the ground, the height (s) is zero.

0 = 2 + 4.9t²

4.9t² = -2

t² = -2/4.9

Taking the square root of both sides, we get:

t ≈ √(-2/4.9)

Since the square root of a negative number is imaginary, it means that the stone does not strike the ground. However, in reality, the stone will strike the ground due to air resistance, which is not considered in this idealized scenario.

Therefore, the time taken by the stone to strike the ground is not defined in this case.

no offence but you all are wrong , initial displacement s= 1/2 at^2 , s= 1/2. 2 .(1) s=1 now initial velocity of rock u=at, or v=2 , now use s=ut +1/2gt^2 don't forget velocity/acceleration/displacement all are vectors so put values accordingly s and g positive and u negative. your welcome