Answer:
Explanation:
From the question we are told that
Constant speed =48mile/hr
Diameter of a wheel = 22inch therefore [tex]r=\frac{22}{2} =>11[/tex]
Generally Convert from mile/hr to inches/sec
The length in inches is equal to the miles multiplied by 63,360.
an hour is 3600seconds
[tex]\frac{48*63360}{3600}[/tex]
48miles/h = 849.8 inch/sec
[tex]V_a =844.8 inch/sec[/tex]
therefore
[tex]\omega= \frac{v}{r}[/tex]
[tex]\omega= \frac{844,8}{11}[/tex] =>[tex]76.8 sec ^-^1[/tex]
a)Considering the velocity of Vb in inches per seconds
Generally the formula is stated as
[tex]V_b= V_a + V_b_/_a[/tex]
[tex]V_b = 844.8 + \omega r[/tex]
[tex]V_b= 1639.6in/s[/tex]
b)Considering the velocity of Vc in inches per seconds
Since the tire doesn't slip as earlier stated in the question
Therefore [tex]V_c = 844.8 -w(r) =0[/tex]
c)Considering the velocity of Ve in inches per seconds
Generally the formula is stated as
[tex]V_e=V_a + V_e_/_a[/tex]
[tex]V_e = 844.8 \uparrow \theta -844.8 \uparrow = 844.8\sqrt{2}[/tex]
Expressing result with vector
[tex]V_e =844.54 + 20.85j[/tex]
d)Considering the velocity of Vd in inches per seconds
Generally the formula is stated as
[tex]V_d= V_a + V_d_/_a[/tex]
Mathematically
[tex]V_d =844.8 \uparrow +( 844.8\frac{\sqrt{3} }{2} \uparrow + \frac{844.8}{2} \uparrow)[/tex]
[tex]V_d= (1576.4 \uparrow + 422.4\uparrow)[/tex]
[tex]V_d= 1632.028in/s[/tex]
