To solve this problem, we need to understand the concept of projectile motion and how it relates to the range of a projectile.

Projectile motion is the motion of an object that is launched into the air and moves along a curved path under the influence of gravity, with no other forces acting on it except for the initial velocity. The path followed by the projectile is called its trajectory.

The range of a projectile is the horizontal distance it travels before hitting the ground again. It depends on the initial velocity of the projectile and the angle at which it is launched.

Given that the range of the projectile is R when the angle of projection is 30 degrees, we need to find the value of the other angle of projection that will result in the same range.

Let's consider two angles of projection: 30 degrees and θ (the other angle we need to find). The initial velocities of the projectile at these angles of projection will be the same, as the problem states that the range is the same for both angles.

We can break down the initial velocity into its horizontal and vertical components. The horizontal component will remain the same for both angles, while the vertical component will change.

Since the range depends on the horizontal component of velocity, which remains constant, we can write:

R = (initial horizontal velocity) * (time of flight)

To find the time of flight, we need to consider the vertical motion of the projectile. The time of flight can be calculated using the formula:

time of flight = (2 * initial vertical velocity) / g

where g is the acceleration due to gravity.

Since the initial velocities at both angles are the same, the time of flight will also be the same.

Now, let's consider the vertical component of the initial velocity. At an angle of 30 degrees, it can be represented as:

initial vertical velocity = (initial velocity) * sin(30)

Similarly, at an angle of θ, it can be represented as:

initial vertical velocity = (initial velocity) * sin(θ)

Since the time of flight is the same for both angles, we can write:

(initial velocity) * sin(30) = (initial velocity) * sin(θ)

Simplifying the equation, we find:

sin(30) = sin(θ)

To find the value of θ that satisfies this equation, we can take the inverse sine (or arcsine) of both sides:

30 = θ

Therefore, the value of the other angle of projection for the same range is 30 degrees.

So, option B, 60 degrees, is the correct answer.

It would be 60
as sin 2(theta)= sin 2 (90-theta)