Projectile Motion: Speed-Solving Techniques (2)

Question

A projectile is launched at angle $60°$ with the horizontal at speed 20 m/s. Find: (a) maximum height, (b) range, (c) time of flight, (d) speed at the highest point. Take $g = 10$ m/s². Solve in under 60 seconds using direct formulas — no kinematics derivations.

Solution — Step by Step

Why This Works

The four formulas — $H$, $T$, $R$, and apex speed — are derived once, then memorized. They handle any projectile launched from ground level on level ground. For projectiles from heights or onto inclined planes, you need the full kinematics, but these direct formulas cover the majority of JEE Main and NEET questions.

The horizontal velocity is unchanged throughout flight (no horizontal force). At the apex, vertical velocity is zero. So apex speed equals horizontal component, always.

Alternative Method

Vector decomposition + kinematics: $y = u_y t - \frac{1}{2}g t^2$, $x = u_x t$. Set $y = 0$ for time of flight, plug into $x$ for range, find $t$ when $v_y = 0$ for max height. Three steps to derive everything from scratch — but slow under exam pressure.

Common Mistake