To find the speed of the falling brush after 2.7 seconds, we can use the equation of motion:
v = u + at
where:
v = final velocity (speed) of the brush
u = initial velocity of the brush (in this case, the brush was dropped and has an initial velocity of 0 m/s)
a = acceleration due to gravity (9.8 m/s^2)
t = time (2.7 seconds)
Plugging in the values, we have:
v = 0 + 9.8 * 2.7
v = 26.46 m/s
The speed of the falling brush after 2.7 seconds is approximately 26.46 m/s.
To calculate the distance the brush has fallen in that time, we can use the equation:
s = ut + 1/2 * a * t^2
where:
s = distance fallen
u = initial velocity of the brush (0 m/s)
a = acceleration due to gravity (9.8 m/s^2)
t = time (2.7 seconds)
Plugging in the values, we have:
s = 0 * 2.7 + 1/2 * 9.8 * (2.7)^2
s = 35.37 m
Therefore, the brush has fallen approximately 35.37 meters in 2.7 seconds.