C

Step 1: For a projectile launched at an angle, the velocity can be broken into two components: horizontal and vertical. The maximum height occurs when the vertical component of the velocity is zero.

Step 2: At maximum height, the velocity is only the horizontal component which remains constant throughout the flight.

Step 3: At half the maximum height, the vertical component has decreased, and the total velocity can be calculated using the components.

Step 4: When the ball returns to the ground, the change in velocity is equal to the initial velocity vector. Thus:

• A corresponds to I (Velocity at half of the maximum height is ).
• B corresponds to II (Velocity at the maximum height is the horizontal component only).
• C corresponds to III (Change in its velocity when it returns to the ground is equal to the initial launch velocity).
• D corresponds to IV (Average velocity when it reaches maximum height is half the initial velocity).

Therefore, the correct mapping is A-I, B-II, C-III, D-IV.