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Home Minds On Vectors and Projectiles Mission VP10 Displacement and Time for a Projectile Help Help 8

Mission VP10 Displacement and Time for a Projectile

The Question

A ball is thrown with a horizontal velocity of 25 m/s from the edge of a 85-meter high cliff. After 2 seconds, the ball will be approximately ____ meters down range (horizontal displacement).

(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

Bright Idea

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. Thus, horizontal motion parameters cannot be mixed with vertical motion parameters when using the equations. Because of this, the vertical height of the cliff has no bearing upon the calculation of the horizontal displacement after 2 seconds of time.

Think About It

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

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