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Home Minds On Vectors and Projectiles Mission VP10 Displacement and Time for a Projectile Help Help 9

Mission VP10 Displacement and Time for a Projectile

The Question

Tom the cat is chasing Jerry the mouse on a table. Jerry puts on the brakes and stops and Tom continues right off the edge of the table at 4.00 m/s. If it takes Tom 0.50 seconds to hit the ground, then the table is approximately ____ meters high and Tom hit the ground a horizontal distance of ____ meters from the table's edge.

(Note: Numbers are randomized numbers and likely different from the numbers listed here.)

Formula Fix

The horizontal displacement (dx) of an object after a certain time (t) can be related to the horizontal acceleration (ax) and the original horizontal velocity (vox) using the kinematic equation:
 
dx = vox• t + 0.5 • ax• t2
 
For a projectile, the horizontal acceleration is 0 m/s/s. Thus, the second term on the right side of the equation can be neglected:
 
dx = vox• t + 0.5 • ax• t2



The vertical displacement (dy) of 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 a projectile whose initial direction of motion is horizontally, the original vertical velocity is 0 m/s. Thus, the first term on the right side of the equation can be neglected.
dy = voy• t + 0.5 • ay • t2

Define Help

Kinematic equations (in Formula Frenzy section) can be used to relate the displacement of a projectile to other motion parameters. When using such equations, it is critical to apply them to the horizontal and vertical motion separately. These two motions are simultaneous and independent of each other and thus horizontal motion parameters cannot be mixed with vertical motion parameters when using the equations. The given value of the original velocity is a horizontal parameter; it should not be used in a vertical equation. As seen in the kinematic equations above, all that is needed to determine the vertical displacement (height of the table) is the time and the acceleration (use the approximate value of 10 m/s/s).

Think About It

Physics formulas can serve as recipes for problem-solving. The substitution of known values of time, original velocity and acceleration into the equations can allow a student to determine the horizontal and vertical displacement.

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