Answer:
Explanation: This is done using the equation:

Because the Radius is a know value. We have the following.

Which is:
4188.7902 mm
 
        
             
        
        
        
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
= final position
 = initial 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 value of spring constant and the oscillator's damping constant is 
K= 6605.667008, b= 0.002884387
Explanation:
For Weakly damping spring oscillator
K/m = W_0^2     (at resonance)
K= mW_0^2
=0.206 * ( 2π * 28.5) ^2
=0.206 * (2π)^2 * (28.5)^2
K= 6605.667008
F = - bV
b= -F/V = -F/ -W_0 * m
=F/W_0 * m
= 0.438N / 2π * 28.5 * 0.848
b= 0.002884387
 
        
             
        
        
        
Answer:
The force required to move the cart is divided by three or 33.33 N.
Explanation: