**Given information:**
- The ball is thrown with a velocity of 7 m/sec.
- The angle of projection is 45 degrees with the horizontal.
- The height of each pole is 90 cm.

**Finding the separation between two poles:**

To find the separation between the two poles, we can break down the problem into horizontal and vertical components.

Let's consider the horizontal and vertical components of the initial velocity:

- Horizontal component: v₀x = v₀ * cos(θ)
- Vertical component: v₀y = v₀ * sin(θ)

For the given problem, the angle of projection is 45 degrees. Therefore, the horizontal and vertical components of the initial velocity are:

- Horizontal component: v₀x = 7 m/sec * cos(45°) = 7 * (√2 / 2) = 7 * 0.707 = 4.95 m/sec
- Vertical component: v₀y = 7 m/sec * sin(45°) = 7 * (√2 / 2) = 7 * 0.707 = 4.95 m/sec

Since the ball just clears the poles, the vertical displacement at the highest point of flight will be equal to the sum of the heights of the two poles.

- Vertical displacement at the highest point: H = 2 * 90 cm = 180 cm = 1.8 m

Using the equation for vertical motion, we can find the time taken for the ball to reach the highest point:

- v = u + at
- v = 0 (at the highest point)
- u = v₀y = 4.95 m/sec
- a = -9.8 m/sec² (acceleration due to gravity)
- t = ? (time taken to reach the highest point)

0 = 4.95 - 9.8 * t
4.95 = 9.8 * t
t = 4.95 / 9.8 = 0.505 sec

Since the time of flight to reach the highest point is the same as the time taken to descend to the same height, the total time of flight is twice the time to reach the highest point:

- Total time of flight: T = 2 * 0.505 sec = 1.01 sec

Now, we can find the horizontal displacement using the equation for horizontal motion:

- Horizontal displacement: S = v₀x * T
- S = 4.95 m/sec * 1.01 sec = 4.9995 m

Therefore, the separation between the two poles is approximately 4.9995 meters.