Question

A ball is dropped from a tower of height \(80\,\text{m}\). The time it takes to cover the last \(50\%\) of its fall is (acceleration due to gravity \(=10\,\text{m s}^{-2}\))

• A. \(2\sqrt{2}\,\text{s}\)
• B. \(1.17\,\text{s}\)
• C. \(4\,\text{s}\)
• D. \(2.0\,\text{s}\)

Hint:

In free fall from rest, \[ s=\frac{1}{2}gt^2. \] To find the time taken for a specific part of the journey, first find the times corresponding to the starting and ending positions and then subtract them.

Answer 1

The Correct Option is B

Step 1: Compute total fall time using kinematics.
h = ½gt² → 80 = 5t² → t = 4 s.

Step 2: Find time to fall first 40 m from top.
40 = 5t₁² → t₁ = 2√2 ≈ 2.828 s.

Step 3: Time for last 40 m = total – first half.
t_last = 4 – 2√2 ≈ 4 – 2.828 = 1.17 s.

Step 4: Final Answer:
1.17 s.