To set a speed record in a measured ( straight-line) distance d, a race car must be driven first in one direction ( in time `t_(1)`) and then in the opposite direction ( in time `t_(2)` ). (a) To eliminate the effects of the wind and obtain the car's speed `v_(c)` in a windless situation, should we find the average of `d//t_(1)` and `d//t_(2)` ( method 1) or should we find divide d by the average of `t_(1)` and `t_(2)` ? (b) What is the fractional difference in the two methods when a steady wind blows along the car's route and the ratio of the wind speed `v_(w)` to the car's speed `v_(c)` is 0.0240 ?

Answer

(a) method 1 gives the car's speed `v_(c)` a in windless situation; (b) `5.76xx10^(_4)`