Question

If a freely falling body covers 80 m in the first 4 seconds, then in the next 4 seconds it covers a distance of:

• A. 160 m
• B. 240 m
• C. 320 m
• D. 80 m
• E. 100 m

Hint:

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.

Answer 1

The Correct Option is B

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.