Question

Two projectiles of identical mass are projected with same initial speed $u$ and angle $\alpha$ in the same plane. They collide at the highest point of their trajectories and stick to each other. Which statement is correct? 

• A. The momentum of the combined object immediately after collision is zero.
• B. Kinetic energy is conserved.
• C. The combined object moves vertically downward.
• D. The combined object moves in a parabolic path.

Hint:

Symmetric projectile collisions often cancel horizontal momenta, leaving only vertical motion.

Answer 1

The Correct Option is A, C

Step 1: Velocities at highest point.
At the top of trajectory: horizontal velocity = $u\cos\alpha$, vertical velocity = 0. Both projectiles have identical horizontal velocities.

Step 2: Collision.
They collide and stick → perfectly inelastic. Total momentum = horizontal momentum of each added: $2m(u\cos\alpha)$. Vertical momentum = 0.

Step 3: After collision.
Immediately after sticking, the combined mass $2m$ has ONLY horizontal velocity. But then gravity acts downward. Thus motion becomes vertical downward (since horizontal velocity cancels due to symmetry?). Actually momentum cancels if one projectile comes from left and one from right. Given the figure shows symmetric angles, momenta cancel. Thus the body moves vertically downward.

Step 4: Conclusion.
Correct: (C).