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Home Minds On Vectors and Projectiles Mission VP10 Displacement and Time for a Projectile Help Help 3

Mission VP10 Displacement and Time for a Projectile

The Question

Two projectiles are launched horizontally from the same initial height at different speeds. Projectile A is launched with a speed of 4 m/s and projectile B is launched with a speed of 12 m/s. Compared to projectile A, projectile B will take ___ to hit the ground.

Physics Rules

Independence of Perpendicular Components of Motion
Perpendicular components of an object's motion are independent of each other. In this module of Minds On Physics, we see this principle in operation in riverboat questions and in projectile questions. For a projectile, the time to fall vertically will be dependent only upon vertical parameters of motion and NOT dependent upon horizontal parameters of motion. The vertical variables that affect the time to fall are the variables found in the kinematic equations (see Formula Frenzy section).

Minds On Time

The only difference between the two projectiles is the initial horizontal speed. Projectile B's horizontal speed is three times greater than projectile A's. The vertical distance fallen is the same for each projectile - that is, they have the same initial height and fall to the same ground. The vertical acceleration is the same for each projectile; it's -9.8 m/s/s for all projectiles. And the initial vertical velocity is the same for each projectile (see A Very Fine Detail section).
 
Now it's minds-on time. Get a mental grip on three ideas and put them together to answer the question: First, perpendicular components of motion are independent of each other (Know the Law section). Second, while projectiles A and B have different horizontal components of motion, they have the same vertical components of motion. Falling is a vertical thingand the time to fall is dependent upon vertical parameters of motion.

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

A Very Fine Detail

The projectile described in this question is "launched horizontally." The significance of these two small words is that the original vertical velocity (voy) 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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