Answer:
A) 12.57 m
B) 5 RPM
C) 3.142 m/s
Explanation:
A) Distance covered in 1 Revolution:
The formula that gives the relationship between the arc length or distance covered during circular motion to the angle subtended or the revolutions, is given as follows:
s = rθ
where,
s = distance covered = ?
r = radius of circle = 2 m
θ = Angle = 2π radians (For 1 complete Revolution)
Therefore,
s = (2 m)(2π radians)
<u>s = 12.57 m</u>
B) Angular Speed:
The formula for angular speed is given as:
ω = θ/t
where,
ω = angular speed = ?
θ = angular distance covered = 15 revolutions
t = time taken = 3 min
Therefore,
ω = 15 rev/3 min
<u>ω = 5 RPM</u>
C) Linear Speed:
The formula that gives the the linear speed of an object moving in a circular path is given as:
v = rω
where,
v = linear speed = ?
r = radius = 2 m
ω = Angular Speed in rad/s = (15 rev/min)(2π rad/1 rev)(1 min/60 s) = 1.571 rad/s
Therefore,
v = (2 m)(1.571 rad/s)
<u>v = 3.142 m/s</u>
Given that,
Time = 0.5 s
Acceleration = 10 m/s²
(I). We need to calculate the speed of apple
Using equation of motion
Where, v = speed
u = initial speed
a = acceleration
t = time
Put the value into the formula
(III). We need to calculate the height of the branch of the tree from the ground
Using equation of motion
Put the value into the formula
(II). We need to calculate the average velocity during 0.5 sec
Using formula of average velocity
Where, 
= final position
= initial position
Put the value into the formula
Hence, (I). The speed of apple is 5 m/s.
(II). The average velocity during 0.5 sec is 2.5 m/s
(III). The height of the branch of the tree from the ground is 1.25 m.
The <em>gaseous state</em> of matter does that. A gas expands to take the shape and volume of whatever you put it into.
