Kinematics

Step 1: Understanding the position and velocity.
The position of the object is given by: To find the acceleration, we need the second derivatives of and . The velocity components in polar coordinates are: The acceleration components are: Step 2: Calculate the velocity components.
The time derivative of is: The time derivative of is: Step 3: Calculate the acceleration components.
Now, calculate the second derivatives: Substitute these derivatives at and solve for the total acceleration.
Step 4: Conclusion.
The magnitude of the acceleration at is approximately 1 m/s .

Step 1: Velocities at highest point.
At the top of trajectory: horizontal velocity = , 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: . Vertical momentum = 0.

Step 3: After collision.
Immediately after sticking, the combined mass 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).