Physics · Class 11 · JEE · 4 October 2026
Projectile motion: 6 traps JEE keeps setting
Projectile questions look easy until the options are built from the mistakes everyone makes. These are the six that come up again and again, with the quick check that catches each one.
1. Complementary angles give the same range
Range on level ground is R = u² sin 2θ / g. Since sin 2θ = sin(180° − 2θ), angles θ and 90° − θ give the same range: 30° and 60° land at the same spot, but 60° goes higher and stays in the air longer. If an option says the 60° throw goes further, it is the trap.
2. Speed at the top is not zero
At the highest point only the vertical velocity is zero. The horizontal velocity u cos θ never changes, so the speed at the top is u cos θ and the acceleration is still g, straight down. Questions that ask for kinetic energy at the top want ½m(u cos θ)².
3. Time of flight depends only on the vertical part
On level ground T = 2u sin θ / g. The horizontal speed has nothing to do with how long the ball stays up. Two balls with the same u sin θ land at the same time, however fast they move sideways.
4. 45° is the best angle only on level ground
Maximum range at 45° assumes the ball lands at the height it was launched from. Thrown from a cliff or a building, the best angle is less than 45°, and you must solve the full equation y = h + (u sin θ)t − ½gt² = 0 for the time of flight instead of using 2u sin θ / g.
5. A neat link between height and range
Dividing H = u² sin²θ / 2g by R = u² sin 2θ / g gives H/R = tan θ / 4, so H = (R tan θ)/4. At 45° the maximum height is exactly a quarter of the range. It is a fast way to check an answer or eliminate options.
6. Horizontal launch from a height
Thrown horizontally from height h, the ball is in the air for t = √(2h/g) — exactly as long as one simply dropped from the same height. The horizontal speed only changes where it lands: x = u√(2h/g).
Practise it
A 10-second check for any projectile answer: the time of flight must use only the vertical component, the range must be the same for θ and 90° − θ on level ground, and the speed anywhere must be at least u cos θ.