Kerala KEAM 5 June 2024 Solved Paper

For a freely falling body, the distance traveled in time $t$ is given by the equation: $$s = ut + \frac{1}{2} g t^2$$where:- $u$ is the initial velocity (which is 0 for a freely falling body),- $g$ is the acceleration due to gravity ($g \approx 9.8 \, m/s^2$),- $t$ is the time.In the first 4 seconds, the body travels a distance of 80 m. Using the formula, we can write: $$80 = 0 + \frac{1}{2} g (4)^2$$ $$80 = \frac{1}{2} g \cdot 16$$ $$g = \frac{80 \times 2}{16} = 10 \, m/s^2$$So, the value of $g$ is approximately $10 \, m/s^2$.Now, in the next 4 seconds, the body continues to fall, and the distance covered in the next 4 seconds can be calculated as follows:The total distance traveled in 8 seconds: $$s = \frac{1}{2} g (8)^2 = \frac{1}{2} \times 10 \times 64 = 320 \, m$$The distance covered in the next 4 seconds is the difference between the total distance covered in 8 seconds and the distance covered in the first 4 seconds: $$Distance in next 4 seconds = 320 - 80 = 240 \, m$$Thus, the correct answer is option (B), 240 m. Quick Tip: In problems involving freely falling bodies, use the kinematic equation $s = ut + \frac{1}{2} g t^2$ to find the distance traveled over a given time. Ensure to use the correct value for acceleration due to gravity.