Answer:
Explanation:
From the question we are told that
Constant speed =48mile/hr
Diameter of a wheel = 22inch therefore ![r=\frac{22}{2} =>11](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B22%7D%7B2%7D%20%3D%3E11)
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
![\frac{48*63360}{3600}](https://tex.z-dn.net/?f=%5Cfrac%7B48%2A63360%7D%7B3600%7D)
48miles/h = 849.8 inch/sec
![V_a =844.8 inch/sec](https://tex.z-dn.net/?f=V_a%20%3D844.8%20inch%2Fsec)
therefore
![\omega= \frac{v}{r}](https://tex.z-dn.net/?f=%5Comega%3D%20%5Cfrac%7Bv%7D%7Br%7D)
=>![76.8 sec ^-^1](https://tex.z-dn.net/?f=76.8%20sec%20%5E-%5E1)
a)Considering the velocity of Vb in inches per seconds
Generally the formula is stated as
![V_b= V_a + V_b_/_a](https://tex.z-dn.net/?f=V_b%3D%20V_a%20%2B%20V_b_%2F_a)
![V_b = 844.8 + \omega r](https://tex.z-dn.net/?f=V_b%20%3D%20844.8%20%2B%20%5Comega%20r)
![V_b= 1639.6in/s](https://tex.z-dn.net/?f=V_b%3D%201639.6in%2Fs)
b)Considering the velocity of Vc in inches per seconds
Since the tire doesn't slip as earlier stated in the question
Therefore ![V_c = 844.8 -w(r) =0](https://tex.z-dn.net/?f=V_c%20%3D%20844.8%20-w%28r%29%20%3D0)
c)Considering the velocity of Ve in inches per seconds
Generally the formula is stated as
![V_e=V_a + V_e_/_a](https://tex.z-dn.net/?f=V_e%3DV_a%20%2B%20V_e_%2F_a)
![V_e = 844.8 \uparrow \theta -844.8 \uparrow = 844.8\sqrt{2}](https://tex.z-dn.net/?f=V_e%20%3D%20844.8%20%5Cuparrow%20%5Ctheta%20-844.8%20%5Cuparrow%20%3D%20844.8%5Csqrt%7B2%7D)
Expressing result with vector
![V_e =844.54 + 20.85j](https://tex.z-dn.net/?f=V_e%20%3D844.54%20%2B%2020.85j)
d)Considering the velocity of Vd in inches per seconds
Generally the formula is stated as
![V_d= V_a + V_d_/_a](https://tex.z-dn.net/?f=V_d%3D%20V_a%20%2B%20V_d_%2F_a)
Mathematically
![V_d =844.8 \uparrow +( 844.8\frac{\sqrt{3} }{2} \uparrow + \frac{844.8}{2} \uparrow)](https://tex.z-dn.net/?f=V_d%20%3D844.8%20%5Cuparrow%20%2B%28%20844.8%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%20%5Cuparrow%20%2B%20%5Cfrac%7B844.8%7D%7B2%7D%20%5Cuparrow%29)
![V_d= (1576.4 \uparrow + 422.4\uparrow)](https://tex.z-dn.net/?f=V_d%3D%20%281576.4%20%5Cuparrow%20%2B%20422.4%5Cuparrow%29)
![V_d= 1632.028in/s](https://tex.z-dn.net/?f=V_d%3D%201632.028in%2Fs)