Question

To set a speed record in a measured (straight-line) distance d, a race car must be driven first in one direction (in time t1) and then in the opposite direction (in time t2). (a) To eliminate the effects of the wind and obtain the car's speed vc in a windless situation, what number of method should we use: the average of d/t1 and d/t2 (method 1) or should we divide d by the average of t1 and t2 (method 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 vw to the car's speed vc is 0.0440?

Answer 1

Suppose the wind is in favor during up journey.
It takes \(t_1\) time to reach the destination in favoring wind :
\[\large V_c + V_w = \dfrac{d}{t _1}\tag{1} \]

and it takes \(t_2\) time to return back in resisting wind :

\[\large V_c - V_w = \dfrac{d}{t _2}\tag{2} \]

Answer 2

Adding both equations you get
\[\large 2V_c = \dfrac{d}{t_1} + \dfrac{d}{t_2}\]

Answer 3

thank you :)

Answer 4

yw :) you could do the rest of problem ?

Answer 5

yeah thanks :)