What is a seed's vertical impact speed after it is launched horizontally from a height of 1 m?

Question

Pressure rises sharply inside the fruit of the squirting cucumber (Ecballium elaterium) as it ripens. When touched, the fruit detaches from its stalk and ejects seeds with its internal liquid.

Assume the seeds leave the fruit 1 m above the ground at an initial speed of 11 m/s relative to the ground, at various angles to the horizontal. Neglect air resistance and wind; take g = 10 m/s². One seed has a mass of 0.07 g and is ejected horizontally. Find the magnitude of its vertical velocity just before it hits the ground. Give the answer in m/s, rounded to one decimal place.

Explanation

The seed is launched horizontally, so its initial vertical velocity is v₀y = 0. For a fall through height h without air resistance:

vᵧ² = v₀y² + 2gh = 2gh.

Using h = 1 m and g = 10 m/s²:

|vᵧ| = √20 ≈ 4.472 m/s ≈ 4.5 m/s.

The horizontal speed of 11 m/s and the seed's mass do not affect this vertical component.