At a construction site a pipe wrench struck the ground with a speed of 24 m/s. (a) From what height was it inadvertently dropped? (b) How long was it falling?
To solve this problem, we can use the equations of motion for free-falling objects.
(a) To determine the height from which the pipe wrench was dropped, we can use the equation:
v² = u² + 2as
where:
v = final velocity (0 m/s as it hits the ground)
u = initial velocity (24 m/s, as given in the question)
a = acceleration due to gravity (-9.8 m/s², assuming downward direction)
s = height or displacement
Rearranging the equation, we get:
s = (v² - u²) / (2a)
Now, let's plug in the values:
s = (0² - 24²) / (2 * -9.8)
Simplifying:
s = (-576) / (-19.6)
s ≈ 29.4 meters
Therefore, the pipe wrench was inadvertently dropped from a height of approximately 29.4 meters.
(b) To calculate the time it took for the pipe wrench to fall, we can use the equation:
s = ut + (1/2)at²
where:
t = time
s = height or displacement (which we just found as 29.4 meters)
u = initial velocity (24 m/s)
a = acceleration due to gravity (-9.8 m/s²)
Rearranging the equation, we get:
t² - (2s/a) = 0
Simplifying:
t² - (2 * 29.4 / -9.8) = 0
t² - 6t = 0
Factoring:
t(t - 6) = 0
Therefore, t = 0 or t = 6
Since time cannot be negative, the time it took for the pipe wrench to fall is approximately 6 seconds.