Question
A particle is projected from the ground with speed m/s at an angle of above horizontal. A wall stands m away. Find the height at which the particle strikes the wall and whether it is still rising or falling at that instant. Take m/s.
Solution — Step by Step
Horizontal: m/s. Vertical: m/s. The horizontal motion is uniform; the vertical motion has acceleration .
The wall is m away, so s. We use horizontal motion because that’s the only equation where time and distance link cleanly.
So the particle hits the wall at roughly 14.64 m above the ground.
Vertical velocity at s is m/s. The negative sign tells us it is falling when it strikes the wall.
Why This Works
Projectile motion always splits into two independent 1D problems — uniform horizontal and uniformly accelerated vertical. The link between them is time. Once we know from horizontal motion, we plug it into the vertical equation and the rest is arithmetic.
Students sometimes try to use the trajectory equation directly. That works, but for finding the velocity direction at impact, the time-based method is faster and more intuitive.
Alternative Method
Using the trajectory equation:
Same answer. Pick the method you remember under exam pressure.
Many students forget that , not . Mixing up sine and cosine of is the single most common JEE Main projectile error — it changes the answer drastically.
If the question asks “rising or falling,” compute at that instant. Sign of tells you immediately. No need to find peak time.
Final answer: height m, particle is falling.