In projectile motion, why does an object that is vertically dropped down and an object that is horizontally launched reach the ground at the same time?

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Answer 1 · 2018-03-07T22:19:34

Because acceleration due to gravity is #9.8 m/s^2# regardless of any horizontal velocity.

A dropped object accelerates downward at g. The time to the ground is given by

#h = 1/2*g*t^2#

A projectile launched horizontally accelerates downward at g. The time to the ground is given by

#h = v_y*t + 1/2*g*t^2#

where the vertical component of its velocity, #v_y#, is zero. Therefore

#h = v_y*t + 1/2*g*t^2 = 1/2*g*t^2#

One condition: if the ground is not perfectly level from the site of the launch of the projectile to the impact area, that would change things.

I hope this helps,
Steve