You toss a book into your dorm room just clearing a windowsill 4.2m above the ground?

Question

-Assume 1 dimensional motion
- if the book leaves your hand 1.5m above the ground, how fast must it be going when it leaves your hand to just clear the sill?
-How long after it leaves your hand will it hit the floor, 0.87m below the windowsill?

Answer 1

1.) Use Torricelli's equation:
vf^2 = vi^2 + 2ad

Since it "just clears the windowsill", then vf = 0.
d = 4.2 - 1.5 = 2.7m

So:
0 = vi^2 + 2 * -9.8 * 2.7
0 = vi^2 + -52.92
vi^2 = 52.92
vi = 7.27 m/s

b.) Define d in this case to be -.87, since 0 is where your hand is.
d = vi * t + 1/2 * at^2
-.87 = 7.27 * t + -4.9 * t^2
0 = -4.9 * t^2 + 7.27 * t + .87

Quadratic formula: t = (-b +/- (b^2 - 4ac)^1/2)/2a
t = (-7.27 +/- (52.8529 - -17.052) ^1/2)/-9.8
t = 0.7418 +/- -0.853
t = 1.5948 sec (ignore the negative result, solution!)