To find the time after which the coin will strike with the lift, we can use the equation of motion:
h = ut + (1/2)at^2
Where:
h = initial height = 2m
u = initial velocity = 0m/s (since the coin is released, it starts from rest)
a = acceleration = -9m/s² (negative because the lift is moving downwards)
t = time
We know that the final height when the coin strikes the lift is 0m (since it will be on the floor of the lift). Therefore, we can rearrange the equation to solve for time:
0 = (1/2)(-9)t^2 + 0t + 2
Simplifying the equation:
-4.5t^2 + 2 = 0
Dividing both sides of the equation by -4.5:
t^2 = 2/4.5
t^2 = 4/9
Taking the square root of both sides:
t = √(4/9)
t = 2/3
Therefore, the time after which the coin will strike with the lift is 2/3 seconds.