an object fall from rest of total height h and covers a distance of h/2 in last second find out time it remain in air

To find the time the object remains in the air, we can use the equation of motion for an object undergoing free fall. The equation is given as:

h = (1/2) * g * t^2

Where:
h is the total height of the object
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time the object remains in the air

In this case, we can use the information given that the object covers a distance of h/2 in the last second. Let's break it down step by step to find the answer:

1. We know that the distance covered in the last second is h/2. This means that the object covers this distance from the time (t-1) seconds to t seconds.
So, the equation for this distance covered in the last second is:
h/2 = g * (t - 1)^2 - g * t^2

2. Simplifying the equation:
h/2 = g * (t^2 - 2t + 1) - g * t^2
h/2 = g * t^2 - 2g * t + g - g * t^2
h/2 = -2g * t + g

3. Rearranging the equation:
-2g * t = h/2 - g
-2g * t = (h - 2g)/2

4. Solving for t:
t = (h - 2g)/(2 * -g)

Now, we can substitute the value of g (approximately 9.8 m/s^2) into the equation and solve for t.