Final answer:
The trajectory of a heavy particle projected at an angle in a uniform gravitational field forms a parabola. This is due to the constant horizontal velocity and the acceleration due to gravity affecting the vertical velocity, resulting in a parabolic path.
"the correct option is approximately option C"
Step-by-step explanation:
The question asks about the trajectory of a heavy particle projected with a velocity at an angle in a uniform gravitational field. When a particle is launched in such a manner, its motion can be broken into two independent one-dimensional motions. Recalling projectile motion concepts, the horizontal motion of the particle is unaffected by gravity, which means that the acceleration along the x-axis (ax) is zero, and thus the horizontal velocity (vx) remains constant.
However, in the vertical axis, the particle is affected by Earth's gravitational pull, which imparts a downward acceleration to the particle. This vertical acceleration is responsible for the parabolic shape of the trajectory, as the vertical velocity increases in magnitude while the particle rises until it reaches its highest point where the vertical velocity becomes zero. Then, as it falls back to Earth, the vertical velocity increases again in magnitude but in the opposite direction. Combining these vertical and horizontal motions results in the overall path of the particle: a parabola.
Therefore, the slope of the trajectory of the particle varies with its horizontal displacement x in a parabolic manner, making option (c) Parabolic the correct answer.