V=20i-gtj=20i-10tj for one and for other v =-20i-10tj so when they are perpendicular dot product of these is zero and we get -400+100t=0. so t=4 sec and as horizontal component of velocity remains same , total displacement= 20 ×4+20×4 = 160m

Introduction:

In this scenario, two projectiles are thrown simultaneously from a suitable height with equal speed in opposite horizontal directions. We need to determine the displacement between the projectiles when they are moving perpendicular to each other, given the acceleration due to gravity (g = 10 m/s^2).

Key Points:

To solve this problem, we can consider the motion of each projectile separately and analyze their components of displacements in the perpendicular direction.

1. Initial Conditions:
- Both projectiles are thrown simultaneously.
- Their initial speeds are equal to 20 m/s.
- The acceleration due to gravity is 10 m/s^2.

2. Horizontal Motion:
- Since the projectiles are thrown horizontally, their initial vertical velocities are zero.
- Therefore, the horizontal motion of both projectiles will remain unchanged throughout their flight.

3. Vertical Motion:
- Due to the acceleration due to gravity, both projectiles will experience a downward acceleration of 10 m/s^2.
- The time of flight and maximum heights reached by the projectiles will be the same.

4. Displacement Calculation:
- Let's assume the time of flight for both projectiles is 't'.
- The horizontal displacement for each projectile can be calculated using the formula: d = v * t, where 'v' is the initial horizontal velocity.
- As both projectiles have the same initial velocity and time of flight, their horizontal displacements will be equal in magnitude but opposite in direction.

5. Perpendicular Motion:
- To find the displacement between the projectiles when they are moving perpendicular to each other, we need to consider their vertical displacements.
- The vertical displacement for each projectile can be calculated using the formula: d = (1/2) * g * t^2.
- Since the time of flight and acceleration due to gravity are the same for both projectiles, their vertical displacements will also be equal in magnitude but opposite in direction.

6. Resultant Displacement:
- The displacement between the projectiles when they are moving perpendicular to each other can be found using the Pythagorean theorem.
- The magnitude of the resultant displacement will be the square root of the sum of the squares of the horizontal and vertical displacements for each projectile.
- The direction of the resultant displacement can be determined using trigonometry or vector analysis.

Conclusion:

In summary, when two projectiles are thrown simultaneously from a suitable height with equal speeds in opposite horizontal directions, the displacement between them when they are moving perpendicular to each other can be determined by considering their horizontal and vertical displacements. The magnitudes of these displacements will be equal but opposite in direction, resulting in a resultant displacement that can be calculated using the Pythagorean theorem.