A physics book slides off a horizontal table top with a speed of 1.45m/s . It st

Question

A physics book slides off a horizontal table top with a speed of 1.45m/s . It strikes the floor after a time of 0.380s . Ignore air resistance.

a) Find the height of the table top above the floor.
b) Find the horizontal distance from the edge of the table to the point where the book strikes the floor.
c) Find the horizontal component of the book's velocity just before the book reaches the floor.
d) Find the vertical component of the book's velocity just before the book reaches the floor.
e) Find the magnitude of the book's velocity just before the book reaches the floor.
f) Find the direction of the book's velocity just before the book reaches the floor. (express as anglemesaured below the horizontal)

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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