Question

At high altitude, a body at rest explodes into two equal fragments with one fragment receiving horizontal velocity of 10 m/s. Time taken by the two radius vectors connecting point of explosion of fragments to make 90° is

• A. 105
• B. 45
• C. 2 s
• D. 1 s

Hint:

For problems involving explosions or relative motion, apply the concept of relative velocity and kinematic equations to find the time taken for specific angles or distances.

Answer 1

The Correct Option is C

In this problem, since the two fragments have horizontal velocities, we can use the basic kinematics equations for relative motion. The horizontal velocities of the fragments indicate that we need to consider the motion of the fragments in the horizontal direction. By analyzing the relative motion between the two fragments and the geometry of the problem, we can calculate the time taken for the two radius vectors to make 90°. Using the relative velocity formula, which involves the horizontal velocities of the fragments, and solving for the time, we find:

\[ t = 2 \, \text{s} \] This calculation takes into account the relative motion between the two fragments and the angle formed by their radius vectors.

Hence, the correct answer is (c).