The problem involves an object in free fall from a height of 80 meters with $g = 10 \, \text{m/s}^2$. Let’s analyze the provided statements one by one:

Equations Used:

1. Distance fallen in time $t$:
   $s = \frac{1}{2} g t^2$
2. Velocity at time $t$:
   $v = g t$
3. Total time to fall:
   The total time $T$ to hit the ground is found from:
   $s_{\text{total}} = \frac{1}{2} g T^2 \quad \text{where } s_{\text{total}} = 80 \, \text{m}$ Solving for $T$:
   $T = \sqrt{\frac{2 \times 80}{10}} = \sqrt{16} = 4 \, \text{seconds.}$

Analysis of Statements:

(a) Distance fallen in the first 1 second:

Using $s = \frac{1}{2} g t^2$:
$s = \frac{1}{2} \times 10 \times (1)^2 = 5 \, \text{meters.}$
True.

(b) Distance fallen in the last second:

In the last second, we consider the total distance traveled by the object minus the distance traveled in the first $T-1$ seconds:
$s_{\text{last second}} = s_{\text{total}} - \left(\frac{1}{2} g (T-1)^2\right)$
Substituting $T = 4$:
$s_{\text{last second}} = 80 - \frac{1}{2} \times 10 \times (4-1)^2 = 80 - \frac{1}{2} \times 10 \times 9 = 80 - 45 = 35 \, \text{meters.}$
True.

(c) Velocity after 2 seconds:

Using $v = g t$:
$v = 10 \times 2 = 20 \, \text{m/s.}$
However, the statement claims 10 m/s, which is incorrect.
False.

(d) Velocity upon hitting the ground:

Using $v = g T$:
$v = 10 \times 4 = 40 \, \text{m/s.}$
The statement claims 20 m/s, which is incorrect.
False.

Summary of Truth Values:

• (a) True
• (b) True
• (c) False
• (d) False

Would you like a detailed breakdown of any specific calculation or additional explanation?

Related Questions:

1. How is the total time of free fall calculated using $g$ and height?
2. What is the formula to determine the distance traveled in the $n$-th second?
3. How does air resistance affect free fall calculations like these?
4. How can we derive velocity at a specific time during free fall?
5. What would change if the object was dropped on a different planet with different $g$?

Tip: When solving motion problems, always start with the basic kinematic equations and clearly define known and unknown values.