A car travels at 87.3 km/h on a level road in the positive direction of an x axi

Question

A car travels at 87.3 km/h on a level road in the positive direction of an x axis. Each tire has a diameter of 66.3 cm. Relative to a woman riding in the car and in unit-vector notation, what are the velocity v Overscript right-arrow EndScripts at the (a) center, (b) top, and (c) bottom of the tire and the magnitude a of the acceleration at the (d) center, (e) top, and (f) bottom of each tire? Relative to a hitchhiker sitting next to the road and in unit-vector notation, what are the velocity v Overscript right-arrow EndScripts at the (g) center, (h) top, and (i) bottom of the tire and the magnitude a of the acceleration at the (j) center, (k) top, and (l) bottom of each tire?

Explanation / Answer

Velociry of car

V=87.3*(1000/3600) =24.25 m/s2

acceleration

a=V2/r =24.252/(0.663/2)=1774 m/s2

so

a) 0

b)(24.25 m/s) i

c)(-24 m/s)i

d)0

e)1774 m/s2

f)1774 m/s2

g)(22 m/s)i

h)

angular velocity

W=V/r =24.25/(0.663/2)=73.15 rad/s

Velocity at the top

V=Wd =(73.15*0.663)=48.5 m/s

in unit vector notation

V=(48.5 m/s)i

i) 0 m/s

j)0

k)1.5*103 m/s2

l)1.5*103 m/s2

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