A body in vertical free fall covers half its total distance in the last second of its fall. The total time taken by the body to cover the entire (whole) path is
A 1.414 s B 1.732 s C 2.414 s D 3.414 s
D 3.414 s
To solve this problem, we can use the equations of motion for an object in free fall. The equation we will use is:
d = v₀t + (1/2)gt²
where:
- d is the total distance traveled by the body
- v₀ is the initial velocity of the body (which is zero in this case since it's in free fall)
- t is the time taken
- g is the acceleration due to gravity
In this problem, we are given that the body covers half its total distance in the last second of its fall. Let's denote the total distance as d.
According to the given information, the body covers half of d in the last second. This means that the distance covered in the last second is (1/2)d.
Now, let's consider the time taken to cover the entire distance d. Since half of d is covered in the last second, the time taken to cover that distance is 1 second.
Using the equation of motion, we can substitute the values:
(1/2)d = 0 + (1/2)(9.8)(1)²
Simplifying the equation, we get:
(1/2)d = 4.9
Multiplying both sides by 2 to get rid of the fraction:
d = 9.8
Now, we need to find the total time taken to cover the entire distance d. We can rearrange the equation of motion to solve for t:
d = 0 + (1/2)(9.8)t²
Substituting the value of d, we get:
9.8 = (1/2)(9.8)t²
Dividing both sides by 4.9 to solve for t²:
2 = t²
Taking the square root of both sides to solve for t:
t = √2
Now, we have the total time taken by the body to cover the entire path, which is √2 seconds.
In decimal form, √2 is approximately 1.414.
Therefore, the answer is option A: 1.414 s.