Thrown horizontally from 500 m at 25 m/s

A stone is thrown horizontally at 25 m/s from a hillside 500 m above the ground (g = 10 m/s²). Find the time of flight and the horizontal distance.

Step-by-step

1. t = √(2h/g) = √(2×500/10) = 10
   Free fall vertically: the time to land depends only on the height
2. x = v₀t = 25×10 = 250
   Uniform horizontal motion at constant velocity

Why it works

The two motions happen at the same time and do not affect each other: vertically the stone falls freely, horizontally it moves at a constant speed, so the time of flight is independent of the horizontal speed.

Common mistakes

• Thinking the stone first falls straight down and only then moves horizontally.
• Dividing the total path length by the horizontal speed to get the time.

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