A structural engineer stood on a top of a building releasing a light and heavy object to the ground which of…

1. Analyze the question

The question asks us to compare the time it takes for two objects of different masses (one light, one heavy) to fall from the same height to the ground, assuming air resistance is neglected.

2. Explain the concept

This is a classic problem in kinematics based on Galileo’s Law of Falling Bodies.

When air resistance is neglected, all objects fall towards the Earth with the same constant acceleration, known as the acceleration due to gravity ($g$), which is approximately $9.8 \, \text{m/s}^2$.

The equation of motion for an object falling from rest is:

Since the objects are released from rest, the initial velocity ($u$) is $0$. The equation simplifies to:

Rearranging to solve for time ($t$):

Notice that the mass of the object does not appear in this formula. This means the time taken to fall depends only on the height ($h$) and the acceleration due to gravity ($g$), not on the mass of the object.

3. Show the solution

• Step 1: Identify the variables. Both objects are dropped from the same height ($h$).
• Step 2: Recognize that the acceleration due to gravity ($g$) acts equally on all objects regardless of their mass.
• Step 3: Apply the formula $t = \sqrt{\frac{2h}{g}}$. Since $h$ and $g$ are the same for both objects, the time ($t$) must be the same for both.
• Conclusion: Because mass is not a factor in the absence of air resistance, both the light and heavy objects will hit the ground simultaneously.

4. Identify the answer

The correct statement is that both objects reach the ground at the same time. This corresponds to option A.

5. Exam Tip

Always remember: In a vacuum (or when air resistance is neglected), a feather and a hammer fall at the same rate. If you see a question about falling bodies in JAMB, check if air resistance is mentioned. If it is neglected, mass is irrelevant!