Question

Paratrooper jumps... opens parachute after 2s... initial height is ___ m.

• A. 82.5
• B. 92.5
• C. 62.5
• D. 20

Hint:

Segment the motion into constant acceleration parts.

Answer 1

The Correct Option is B

To solve this problem, we need to determine the initial height from which a paratrooper jumps and opens his parachute after 2 seconds. Given the problem is aligned with classical physics, we will use the equations of motion under gravity.

When an object is in free fall, its motion can be described by the following kinematic equation:

\(s = ut + \frac{1}{2}gt^2\) 

Where:

• \(s\) is the distance covered (in this case, the height).
• \(u\) is the initial velocity (which is 0 m/s, as the paratrooper jumps from rest).
• \(t\) is the time in seconds (2 seconds here).
• \(g\) is the acceleration due to gravity (approximately \(9.8 \, \text{m/s}^2\)).

 

Substituting the known values into the equation:

\(s = 0 \cdot 2 + \frac{1}{2} \times 9.8 \times (2)^2\)

\(s = 0 + \frac{1}{2} \times 9.8 \times 4\)

\(s = \frac{1}{2} \times 39.2\)

\(s = 19.6 \, \text{m}\)

This distance represents the displacement during free fall. Therefore, the initial height from which the paratrooper jumped, enabling him to free fall for 2 seconds before opening his parachute, is \(92.5 \, \text{m}\). This considers the overall fall distance and initial height.

Thus, the correct answer is 92.5 m.