a book slides off a table top with a speed of 18 meters per second. it strikes the floor in 0.52 seconds how tall was the table in meters
how long does it take something to fall for.52 seconds? The horizontal velocity does not change that.
h= 1/2 g t^2 solve for h
To determine the height of the table, we can utilize the equations of motion and the given information.
Firstly, we need to identify what we know:
Initial speed (u) = 0 m/s (since the book was at rest on the table before sliding off)
Final speed (v) = 18 m/s
Time taken (t) = 0.52 seconds
Acceleration (a) = ?
We can use the equation of motion: v = u + at, where:
v = final velocity
u = initial velocity
a = acceleration
t = time
As the book is falling, the acceleration acting on it is due to gravity and can be assumed as about 9.8 m/s^2 (acceleration due to gravity near the Earth's surface).
Now, let's calculate the acceleration:
v = u + at
18 m/s = 0 m/s + 9.8 m/s^2 * 0.52 s
18 m/s = 5.096 m/s
By rearranging the equation, we can solve for "a":
a = (v - u) / t
a = (5.096 m/s - 0 m/s) / 0.52 s
a = 9.8 m/s^2 (approx.)
Now, to find the height of the table, we can use the equation of motion: s = ut + (1/2)at^2, where:
s = distance (height)
u = initial velocity
t = time
a = acceleration
Since the book was at rest on the table before sliding off, the initial velocity is 0 m/s.
s = ut + (1/2)at^2
s = 0 m/s * 0.52 s + (1/2) * 9.8 m/s^2 * (0.52 s)^2
s = 1.2736 m
Therefore, the height of the table is approximately 1.27 meters.