A physics book slides off a horizontal table top with a speed of 1.25 m/s. It st

Question

A physics book slides off a horizontal table top with a speed of 1.25 m/s. It strikes the floor after a time of 0.330s. Ignore air resistance.

* Find the height of the table top above the floor.

*Find the horizontal distance from the edge of the table to the point where the book strikes the floor.

*Find the horizontal component of the book's velocity just before the book reaches the floor.

* Find the vertical component of the book's velocity just before the book reaches the floor.

* Find the magnitude of the book's velocity just before the book reaches the floor.

* Find the direction of the book's velocity just before the book reaches the floor.

*

Explanation / Answer

Since it slides off the table, its horizontal velocity is 1.15 m/s. There is no initial vertical velocity. a) to get height, just plug in the numbers to a kinematic equation x=xi + vt + .5at^2 (x=final position, xi = initial position, v=velocity, t = time, a=-9.8 m/s^2) 0 = xi + 0 + (.5)(-9.8)(.37)^2 xi = .67081 meters b) just multiply the horizontal velocity by time x=xi + vt 1.15 x .37 = .4255 meters c) The horizontal component of the velocity remains the same throughout its flight, so 1.15 m/s d) To find the vertical velocity, we use kinematics v=vi + at (v=final velocity, vi = initial velocity, a=-9.8 m/s^2, t = .37) v = 0 + (-9.8)(.37) = -3.626 m/s e) Use pythagorean theorem for horizontal and vertical (1.15)^2 + (3.626)^2 = x^2 x = 3.80399 m/s f) We can use trigonometry to get direction, since we already have the components tan x = 3.626 / 1.15 x = 72.40337 degrees below the horizontal

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