A car travels at 54.3 km/h on a level road in the positive direction of an x axi

Question

A car travels at 54.3 km/h on a level road in the positive direction of an x axis. Each tire has a diameter of 74.0 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?

Explanation / Answer

relative to woman velocity of centre = 0 top = rw = v = 54.3km/h (i^) in forward direction bottom = -v = -54.3 km/h (i^) (d) acceleration = v^2/r centre = 0 (at rest) e) top = 307.44 m/s^2 in downward direction f) bottom = 307.44 m/s^2 upward direction (g) centre = v = 54.3km/h (i^) in forward direction h) top = 2v = 108.6 km/h (i^) in forward direction i) bottom = 0 acceleration = v^2/r ; j) centre of wheel = 307.44 m/s^2 in downward direction k)top = 2*v^2/r = 614.88 m.s^2 in downward direction l) bottom of the tire = zero .

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