a) While painting a 12 meter high roof you knock the paint brush off the edge, with no air resistance on the brush how long will it take to hit the ground?
b) What would the velocity of the brush be before it hit the ground?
*While painting on a 12 meter high roof,
Please check
12m= (0m/s)+1/2(9.81m/s^2)(t^2)
12m= 0+(4.905m/s^2)(t^2)
t^2=12/4.905m/s^2
t^2= 2.45s^2
t= 1.565 s
t= 1.6 s
Velocity
12/1.6 sec= 7.5 meters/sec down
t= 1.565 s - correct
v =g•t =9.8•1.565 = 15.3 m/s
To determine the time it takes for the paint brush to hit the ground, we can use the equation of motion. In this case, since there is no air resistance, we can assume that the only force acting on the paint brush is gravity. We can use the following equation:
h = (1/2) * g * t^2
where:
h = height of the roof (12 meters)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
To find the time t, we can rearrange the equation:
t^2 = (2 * h) / g
t = sqrt((2 * h) / g)
Plugging in the values:
t = sqrt((2 * 12) / 9.8)
t = sqrt(24 / 9.8)
t = sqrt(2.44)
t ≈ 1.56 seconds
Therefore, it will take approximately 1.56 seconds for the paint brush to hit the ground.
Now let's determine the velocity of the brush before it hits the ground. We can use the equation of motion relating displacement, initial velocity, time, and acceleration:
v = u + g * t
where:
v = final velocity (unknown)
u = initial velocity (unknown)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time (1.56 seconds)
Since the brush starts from rest (initial velocity u is 0), the equation simplifies to:
v = g * t
Plugging in the values:
v = 9.8 * 1.56
v ≈ 15.288 m/s
Therefore, the velocity of the brush before it hits the ground is approximately 15.288 m/s.