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Home Minds On Vectors and Projectiles Mission VP10 Displacement and Time for a Projectile Help Help 2

Mission VP10 Displacement and Time for a Projectile

The Question

A projectile of mass "m" is launched horizontally from an elevated height of "h" meters with an initial speed of "v" m/s. The time for the horizontally-launched projectile to fall to the ground below is dependent upon ...

Formula Fix

The distance fallen (dy) by an object after a certain time (t) can be related to the vertical acceleration (ay) and the original vertical velocity (voy) using the kinematic equation:
 
dy= voy• t + 0.5 • ay• t2
 
For horizontally-launched projectiles, the original vertical velocity is 0 m/s. Thus the equation can be simplified to
 
dy= voy• t + 0.5 • ay• t2

Think About It

The vertical motion of a projectile is independent of the horizontal motion and dependent solely upon vertical information. The time to fall to the ground is dependent upon vertical parameters of motion such as vertical velocity, vertical acceleration and vertical distance of fall. The Formula Frenzy section expresses the interdependency of these variables in the form of an equation. Use the formula to guide your reasoning concerning the answer to this question. (And don't ignore the A Very Fine Detail section.)

A Very Fine Detail

The projectile described in this question is "launched horizontally." The significance of these two small words is that the initial vertical velocity is 0 m/s for a horizontally launched projectile. The initial velocity of the such a projectile is entirely horizontal. Thus, the initial velocity is the initial horizontal velocity; it should not be confused with the vertical velocity.

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