a body travels half of its total path in the last second of its free fall from rest.what is the duration of fall .
you have answered the question before but the answer my mam gave is 3.4sec but you have solved it to 1.4sec .plz solve it for me
To solve this problem, we need to use the equations of motion for an object in free fall. The equation that relates displacement (s), initial velocity (u), time (t), and acceleration due to gravity (g) is:
s = ut + 0.5gt^2
In this problem, the body is at rest initially, so the initial velocity (u) is zero. Also, the body travels half of its total path in the last second of its free fall. This means that the displacement in the last second (s1) is half of the total displacement (s). Using this information, we can set up the equations:
s = s1 + s2
s1 = s/2
Let's substitute the second equation into the first equation:
s = s/2 + s2
Now, let's solve for s2 by rearranging the equation:
s2 = s - s/2
s2 = s/2
Now, let's substitute the value of s2 into the equation of motion:
s = ut + 0.5gt^2
s = 0 + 0.5gt^2
s = 0.5gt^2
Using the information given in the problem, we know that the body travels half of its total path in the last second of its free fall. So, during the last second, the displacement (s1) is half of the total displacement (s). This indicates that the total duration of free fall is double the duration of the last second.
Let's denote the duration of the last second as t1, and the total duration of free fall as t. We have:
t1 = 1 second
t1 = t - 1 second
We need to find the value of t. Substituting the values into the equation of motion:
s = 0.5gt^2
s1 = 0.5g(1^2)
s1 = 0.5g
Also, we know that s1 is half of the total displacement:
s1 = s/2
0.5g = s/2
From these two equations, we can solve for s:
s = g
Now, substituting the value of s back into the equation of motion:
g = 0.5gt^2
g = 0.5g(t^2)
We can simplify by dividing both sides by 0.5g:
1 = t^2
Taking the square root of both sides:
t = 1 second
Therefore, the total duration of free fall is 1 second, not 1.4 seconds as previously stated. Sorry for the earlier incorrect response.
Note: It is essential to double-check calculations and equations when solving physics problems to ensure accuracy. Always verify the results with reliable sources or consult a teacher or expert.