Introduction:
When a particle is projected horizontally with a certain speed (u) from a tower, it follows a parabolic trajectory due to the influence of gravity. In this scenario, the tower is situated on an inclined plane, and the particle is projected perpendicularly to the inclined plane. The question asks us to determine the horizontal speed of the particle.

Understanding the problem:
To solve this problem, we need to consider the motion of the particle in the horizontal and vertical directions separately. The horizontal motion is unaffected by gravity, while the vertical motion is influenced by gravity.

Horizontal motion:
Since the particle is projected horizontally, its initial velocity in the horizontal direction (u_x) is constant throughout its motion. Therefore, the horizontal speed of the particle remains the same.

Vertical motion:
In the vertical direction, the particle experiences the effect of gravity. It will accelerate downwards at a rate of 9.8 m/s² (assuming no air resistance). The initial vertical velocity (u_y) of the particle is zero because it is projected perpendicularly to the inclined plane.

Applying kinematic equations:
We can use the kinematic equations to determine the time taken by the particle to reach the ground. The height of the tower (10 m) can be considered as the displacement in the vertical direction.

Using the equation:
s = ut + (1/2)at²

We can rearrange it to solve for time (t):
10 = 0*t + (1/2)*9.8*t²

Simplifying the equation, we get:
4.9t² = 10

Solving for t:
t² = 10/4.9
t ≈ 1.43 seconds

Calculating horizontal speed:
Since the horizontal speed remains constant throughout the motion, we can calculate it by using the formula:

Horizontal speed (v) = u_x = (Horizontal displacement) / (Time taken)

In this case, the horizontal displacement is the same as the distance traveled by the particle in the horizontal direction, which is determined by the time taken (t) and the horizontal speed (u_x).

Since the particle was projected horizontally, its initial horizontal position and final horizontal position are the same. Therefore, the horizontal displacement can be calculated as:
Horizontal displacement = u_x * t

Substituting the known values:
Horizontal speed (v) = u_x = (u_x * t) / t = u_x

Thus, the horizontal speed of the particle is equal to its initial horizontal speed (u_x).

Conclusion:
When a particle is projected horizontally from a tower on an inclined plane perpendicularly, its horizontal speed remains constant throughout its motion. The horizontal speed is equal to the initial horizontal speed, which is determined by the initial velocity in the horizontal direction.

200m/s