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 t2). (a) to eliminate the effects of the wind and obtain the car's speed vc in a windless situation, should we find the average of d/t1 and d/t2 (method 1) or should we divide d by the average of t1 and t2? (b) what is the fractional difference in the two methods when a steady wind blows along the car's route

solution:

v = speed of car with no wind

u = speed of the wind along the path of the car

v - u = speed when going against the wind

v + u = when going in the same direction as the wind

v - u = d/t1

v + u = d/t2

2v = [d/t1 + d/t2]

v = (1/2) [d/t1 + d/t2]

course the meanings of t1 and t2 are not important equation in exactly the same way

So,

the method to use is method 1.

u/v = 0.0240 so u = 0.024v

Other method v = d/[ (t1 + t2) / 2] = (2) {1/[t1/d + t2/d]}

diff = (1/2) [d/t1 + d/t2] - (2) {1/[t1/d + t2/d]}