Acar travels at 80 km/h on a level road in the positive direction of an x axis. each tire has a diameter of 66 cm. relative to a woman riding in the car and in unit-vector notation, what are the velocity 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 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?

80 km/h = 22.2 m/s
66 cm = 0.66 m

Relative to the woman riding in the car:

(a) Since the center of the tire is not moving, and the woman goes along with the movement of the car, v=0
(b) v = +22.2 km/h, since the wheel turns at this velocity from left to right
(c) v = -22.2 km/h, since the wheel turns at this velocity from right to left
(d) a = 0, since v=0
(e) a = v2/r = (+22.2)^2/(0.66 ÷2) = 1493.45 m2/s
(f) a = v2/r = (-22.2)^2/(0.66 ÷2) = -1493.45 m2/s

Relative to hitchhiker:

(g) v = +22.2 m/s, since from an external body, the velocity of the car is still observed
(h) v = +22.2 x 2 = 44.4 m/s, since the  top runs twice faster to be able to move the car
(i)  v = 0, since from an external body, the bottom part of the tire is always in contact with the ground
(j) a = 0, because velocity is constant
(k) a = 1493.45 m2/s, same with that of the woman because both are inertial reference
(l) a = -1493.45 m2/s, same with that of the woman because both are inertial reference

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