An object rolls off a tabletop with a horizontal velocity v0x = 2.2 m/s. the table is at a height y0 = 0.65 m, above the floor. use a coordinate system with its origin on the floor directly beneath the point where the object rolls off the table, its horizontal x-axis lying directly beneath the object’s trajectory, and its vertical y-axis pointing up. find the angle of impact, in degrees below the horizontal.

58.6 degrees below the horizontal

Explanation:

The horizontal velocity of the object remains constant:

The vertical motion instead is an accelerated motion, so the vertical velocity changes according to

where

is the final vertical velocity

is the initial vertical velocity

g = -9.8 m/s^2 is the acceleration of gravity (downward, so with a negative sign)

d = -0.65 m is the vertical displacement of the object

Solving the equation for ,

The vertical velocity just before the impact is therefore -3.6 m/s (negative since it points downward).

The angle of impact below the horizontal therefore will be

below the horizontal.

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