Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 10

10 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 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?