Projectile from 80 m at 20 m/s

A projectile is launched horizontally from a height of 80 meters with an initial horizontal speed of 20 m/s, taking g = 10 m/s². Find the time it takes to hit the ground and its horizontal displacement.

Step-by-step

1. t = √(2h/g) = √(2×80/10) = 4
   Free fall vertically: the time to land depends only on the height
2. x = v₀t = 20×4 = 80
   Uniform horizontal motion at constant velocity

Why it works

The method for handling projectile motion is decomposition: uniform linear motion in the horizontal direction, free fall in the vertical direction, linked by time. The landing time depends only on height and is independent of initial horizontal speed; horizontal displacement is obtained by multiplying initial speed by this time. Therefore, increasing the initial horizontal speed only changes how far it flies, not when it lands.

Common mistakes

• 1) Thinking that a larger initial horizontal speed means earlier landing, calculating time as dependent on initial speed.
• 2) Using uniform motion formulas for the vertical direction to calculate height or time, missing the one-half factor.
• 3) Using the wrong time when calculating horizontal displacement, using the time from another stage.

Related

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