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A body falls freely from rest under gravity and covers a certain height in the last second of its motion equal to the height covered in the first three seconds. What is the total height from which the body fell? (Take g = 10 m/s²)
125 m
100 m
80 m
150 m
125 m
The distance covered in the first t seconds is given by h=21gt2. The distance covered in the last second of motion is given by hn=u+2g(2n−1), where u=0. Equating these allows us to solve for the total time n and total height H=21gn2.
The distance covered in the first t seconds is given by h=21gt2. The distance covered in the last second of motion is given by hn=u+2g(2n−1), where u=0. Equating these allows us to solve for the total time n and total height H=21gn2.
Think of a ball dropping like a speeding car entering an intersection; the distance it covers in the very last second increases as it gathers speed, just like the gaps between falling raindrops grow larger as they accelerate.
H=21gt2 — Total distance covered in time t
Sn=2g(2n−1) — Distance covered in the nth second
For an object falling from rest (u=0), the distance covered in the nth second is Sn=2g(2n−1). The total distance covered in n seconds is H=21gn2. Setting the distance in the nth second equal to the distance covered in the first 3 seconds (21g(3)2=45 m) allows us to calculate the time n and the total drop height.
Acceleration due to gravity (g) is considered constant at 10 m/s2 for this problem.
Initial velocity (u) is 0 m/s as the body falls from rest.
The total height is proportional to the square of the total time of fall.
Physics kinematics problems
Analysis of free-falling objects
Calculation: 2g(2n−1)=21g(3)2. Simplifying gives 2n−1=9, so 2n=10, n=5 s. Total height H=21(10)(52)=125 m.
Option B (100m), C (80m), and D (150m) are mathematically inconsistent with the kinematic equations of motion for this time frame.
A is correct — The body falls for 5 seconds, resulting in a total height of 125 meters.
Always check if the problem specifies 'in the nth second' (a specific interval) versus 'in n seconds' (total elapsed time), as they yield very different values.
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