Answer:
a
[tex]x = 209.5 \ m[/tex]
b
[tex]t = 13.4 \ minutes[/tex]
c
[tex]t_v = 24 \ minutes[/tex]
Step-by-step explanation:
From the question we are told that
The diameter is d = 120 m
The speed of the wheels is [tex]v = 26 \ cm / s = 0.26 \ m/s[/tex]
Generally the radius is mathematically represented as
[tex]r = \frac{d}{2} = \frac{120}{2} = 60 \ m[/tex]
Generally the circumference is mathematically evaluated as
[tex]C= 2 \pi r[/tex]
[tex]C= 2 * 3.142 * 60[/tex]
[tex]C= 377.04 \ m[/tex]
Generally
C [tex]\to \ 360^o[/tex]
x [tex]\to \ 200^o[/tex]
=> [tex]x = \frac{C * 200}{360}[/tex]
=> [tex]x = \frac{ 377.04* 200}{360}[/tex]
=> [tex]x = 209.5 \ m[/tex]
Generally the angular speed is mathematically evaluated as
[tex]w = \frac{v}{r}[/tex]
=> [tex]w = \frac{0.26}{60}[/tex]
=> [tex]w = 0.00433 \ rad/s[/tex]
Generally
[tex]1 \ radian \to 57.2958^o[/tex]
z radian [tex]\to 200^o[/tex]
=> [tex]z = \frac{200}{57.2958}[/tex]
=> [tex]z = 3.49 \ radian[/tex]
Generally the time taken is mathematically evaluated as
[tex]t = \frac{z}{w}[/tex]
=> [tex]t = \frac{3.49}{0.00433}[/tex]
=> [tex]t = 806.2 \ s[/tex]
Converting to minutes
[tex]t = \frac{806.2}{60}[/tex]
[tex]t = 13.4 \ minutes[/tex]
Generally given that one resolution is equal to 360° so
[tex]1 \ radian \to 57.2958^o[/tex]
v radian [tex]\to 360^o[/tex]
=> [tex]v = \frac{360}{57.2958}[/tex]
=> [tex]v = 6.28 \ radian[/tex]
Generally the time taken is mathematically evaluated as
[tex]t_v = \frac{v}{w}[/tex]
=> [tex]t_v = \frac{6.28}{0.00433}[/tex]
=> [tex]t_v = 1451.1 \ s[/tex]
Converting to minutes
=> [tex]t_v = \frac{1451.1}{60}[/tex]
=> [tex]t_v = 24 \ minutes[/tex]
