physics book slides off a horizontal table top with a speed of 1.35 m/s. It stri

Question

physics book slides off a horizontal table top with a speed of 1.35 m/s. It strikes the floor in 0.500 s. Ignore air resistance. (Assume the book's horizontal direction and upward are positive.)

(a) Find the height of the table top above the floor.
..............m

(b) Find the horizontal distance from the edge of the table to the point where the book strikes the floor.
............m

(c) Find the horizontal and vertical components of the book's velocity just before it reaches the floor.
............m/s (horizontal component)
............m/s (vertical component)

Find the magnitude and direction of the book's velocity just before it reaches the floor.
.......m/s
........

Explanation / Answer

(a)The height of the table top above the floor

h = ut + (1/2)gt2

u = 1.35 m/s,g = 9.8 m/s2 and t = 0.500s

(b)The height from which the book falls can also be writtenas

h = (u2 * sin2?/2g)

solving the above equation for ? we get

? = sin-1[(2g * h)1/2/u]

(b)The horizontal distance from the edge of the table to thepoint where the book strikes the floor

R = (u2 * sin(2?)/g)

(c)The final velocity of the book is

v2 - u2 = 2gh

or v = (u2 + 2gh)1/2

The horizontal and vertical components of the book's velocityjust before it reaches the floor

vx = v * cos? and vy = v *sin?

The magnitude of the book's velocity just before it reachesthe floor

v = (vx2 +vy2)1/2

The direction of the book's velocity just before it reachesthe floor

tan? = (vy/vx)

or ? =tan-1(vy/vx)

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