Three identical spheres are thrown from the same height above the ground. Sphere X is thrown vertically up, sphere Y is thrown horizontally, and sphere Z is thrown vertically down, as shown in Figures 1, 2, and 3 above, respectively. All three spheres are thrown with the same speed. Air resistance is negligible.Assume the spheres collide elastically with the ground. Which of the following ranks the spheres based on the rebound height after they collide with the ground?A) \( X > Y = Z \)B) \( Y > (X = Z) \)C) \( Z > Y > X \)D) \( (X = Z) > Y \)E) \( (X = Z) = Y \) **Title: Analyzing the Motion of Thrown Spheres****Introduction:**In this problem, we examine the motion of three identical spheres, each thrown from the same height above the ground. The spheres are thrown with negligible air resistance, allowing us to focus purely on the physics of their trajectories.**Description of Set-Up:**- **Sphere X**: Thrown vertically upward with an initial speed \(v\). - **Sphere Y**: Thrown horizontally with an initial speed \(v\).- **Sphere Z**: Thrown vertically downward with an initial speed \(v\).All spheres start from the same height \(h\).**Figures Explanation:**- **Figure 1**: Depicts Sphere X with an initial upward velocity \(v\). The height from which it is thrown is marked as \(h\). - **Figure 2**: Illustrates Sphere Y moving horizontally at the same initial speed \(v\). The starting height \(h\) is identical to that of Sphere X. - **Figure 3**: Shows Sphere Z being thrown downward at an initial speed \(v\). It also begins at height \(h\).**Question:**Which sphere or spheres initially collide with the ground with the greatest speed?**Options:**A) Sphere X onlyB) Sphere Y onlyC) Sphere Z onlyD) Spheres X and Z onlyE) All three spheres collide with the same speedUnderstanding the principles of projectile motion and free fall will aid in solving this problem. Consider the conservation of energy and the effects of gravitational acceleration when analyzing the spheres' motions.

Correct options:- (1) (X=Z) > Y (2) Option (E)- All three-sphere collide with the same speed. Explanation- According to the kinematics equation, vf2=vi2+2gh For sphere X, the final velocity in the y-direction is, vy=v2+2gh For sphere Y, the final velocity in the y-direction is the addition of the component of velocity in the horizontal direction and a component of velocity in the vertical direction. The horizontal component remains the same only the vertical velocity component changes with respect to the height. vf2=vx2+vy2 vy=v2+2gh 2vy=v2+2gh For sphere Z, the final velocity in the y-direction is vy=v2+2gh Hence, all three spheres X, Y, and Z collide with the ground at the same speed. Thus option (E) is correct.

Answered: Figure 1 Figure 2 Figure 3 Three…