A student drops his textbook out of a window in a tall building. If it took 1.51 seconds for the book to hit the ground, how high above the ground is the window? What is the book' maximum speed during flight? At what time does this occur?
The window is at a height of 11.2 meters above the ground.
Ok, so let's see if I can do a better job explaining this.
Let's say that the window is alocated at a hight
During its flight, it will be accelerated by the gravitational acceleration,
This means that the distance
#h = underbrace(v_0)_(color(blue)(=0)) * t + 1/2 * g * t^2#
#h = 1/2 * 9.8"m"/color(red)(cancel(color(black)("s"^2))) * 1.51^2 color(red)(cancel(color(black)("s"^2))) = color(green)("11.2 m")#
Since the book keeps accelerating as it falls, it makes sense that it will have a maximum speed right before hitting the ground.
#v^2 = underbrace(v_0^2)_(color(blue)(=0)) + 2 * g * h#
#v^2 = 2 * g * h implies v = sqrt(2 * g * h)#
#v = sqrt(2 * 9.8"m"/"s"^2 * "11.2 m") = color(green)("14.8 m/s")#
Alternatively, you can use the equation
#v = underbrace(v_0)_(color(blue)(=0)) + g * t#
which will produce the same value for
#v = 9.8"m"/"s"^color(red)(cancel(color(black)(2))) * 1.51color(red)(cancel(color(black)("s"))) = "14.8 m/s"#
The book will have maximum velocity after 1.51 seconds of free falling, just before it impacts the ground.