The body is projected with same initial velocity for two projectile. Horizontal range of projectiles is same when the angle of projection are:

The horizontal range (R) of a projectile is given by the equation:

R = (v^2/g) * sin(2θ)

where: v = initial velocity g = acceleration due to gravity θ = angle of projection

Given that the horizontal range is the same for two projectiles with the same initial velocity, we can equate the two equations:

(v^2/g) * sin(2θ1) = (v^2/g) * sin(2θ2)

Solving this equation, we find that:

sin(2θ1) = sin(2θ2)

This equation holds true for two angles if they are complementary, i.e., if they add up to 90 degrees. Therefore, the two angles of projection that would give the same horizontal range for the same initial velocity are two angles that are complementary to each other.

In other words, if one angle is θ, the other angle would be 90 - θ.

The horizontal range (R) of a projectile is given by the equation:

R = (v^2/g) * sin(2θ)

where: v is the initial velocity, g is the acceleration due to gravity, and θ is the angle of projection.

If the horizontal range is the same for two projectiles with the same initial velocity, then the angles of projection must be complementary. This means that the two angles add up to 90 degrees.

So, if one angle is θ, the other angle must be 90 - θ. This is because the sin(2θ) function has the property that sin(2θ) = sin(180 - 2θ), which means that the range will be the same for angles of θ and 90 - θ.

Therefore, the horizontal range of projectiles is the same when the angles of projection are complementary (i.e., they add up to 90 degrees).