Question

The vertical component of velocity of a projectile at its maximum height ($u$ – velocity of projection, $\theta$ – angle of projection) is

• A. $u \sin\theta$
• B. $u \cos\theta$
• C. $\frac{u}{\sin\theta}$
• D. 0
• E. $\frac{u}{\cos\theta}$

Hint:

Total velocity at maximum height is not zero—only the vertical component is. The projectile still moves forward with its constant horizontal velocity $u \cos\theta$.

Answer 1

The Correct Option is D

Concept: Projectile motion consists of two independent components: horizontal motion with constant velocity and vertical motion with constant acceleration ($g$).
• Vertical Component: $v_y = u \sin\theta - gt$.
• At Maximum Height: The vertical motion momentarily stops before the particle begins to descend.

Step 1: Analyze velocity at the peak.
The definition of the "maximum height" of a projectile is the point where its upward vertical velocity has been completely reduced to zero by gravitational acceleration.

Step 2: Identify the remaining velocity.
At this point, only the horizontal component ($u \cos\theta$) remains, as it is unaffected by gravity. Since the question specifically asks for the vertical component at this instant, the value is 0.