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Projectile Motion

Projectile motion involves motion of an object in the horizontal (x) direction and the vertical (y) direction. Motion in one dimension is completely independent of motion in the other direction. For example, acceleration due to gravity does not affect the constant horizontal motion just as the motion in the horizontal direction does not affect the acceleration in the vertical direction. What connects the two motions is the time the projectile is in the air. This can be calculated using the appropriate kinematics equations for the vertical motion.

Horizontally Launched Projectiles:

The initial velocity is entirely in the horizontal direction. There is no vertical (y) component for the initial velocity. Once the object is launched it accelerates towards earth and gains vertical velocity. Since no forces act in the horizontal direction (we neglect air resistance), the horizontal (x) component of the velocity remains constant. Once time is calculated, the range of the projectile can be calculated by multiplying the horizontal velocity by the time.

Projectiles Launched at an Angle:

The direction of the initial velocity is usually measured as an angle with the horizontal. The initial velocity can be broken down into x and y components by multiplying the initial velocity by the appropriate trig functions. As with the horizontally launched projectile, no unbalanced forces act in the horizontal direction so the horizontal velocity remains constant for the entire trip. Since gravity affects the vertical motion and causes acceleration towards the earth, the velocity decreases from the initial velocity to zero, then starts increasing in the downward direction. Once time is calculated, the range of the projectile can be calculated by multiplying the horizontal velocity by the time.

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