A projectile is fired horizontally from a cliff 80 m high with speed 30 m/s. How long does it take to hit the ground? (Take g = 10 m/s²)

Solution

Physics sir · 3 steps

Horizontal speed has nothing to do with the fall time: the 80 m drop alone decides it.

1. Split the motion. Fired horizontally means the initial vertical velocity is zero. The 30 m/s is entirely horizontal, and gravity acts only in the vertical direction.
2. Vertical fall. Vertically, the projectile falls from rest through h = 80 m with acceleration g = 10 m s⁻².

   h = 1/2 g t² ⇒ t = √(2h/g) = √((2 × 80)/10) = √16 = 4 s

3. So. The projectile takes 4 s to hit the ground, option (c). The horizontal speed only decides how far it lands: 30 × 4 = 120 m from the foot of the cliff.

The idea to keep. For a horizontal launch, time of flight is √(2h/g), the same as dropping the object from rest. Horizontal speed changes the range, never the time.

Answer from the NTA final answer key. Solution by PrepWiser.