Question

You know that your kicker can make a field goal from 60 yards away, provided there is no air or wind resistance. This kick is 55 yards away, but there is wind which you expect will give the ball an acceleration in the x-direction of -.3 m/s2 . The coach (who besides knowing a lot about football is very knowledgeable about physics) wants to know if you should go for the kick or not, and your reasoning. What should you tell him?

Answer 1

here,

for maximium range ,

the angle is 45 degree above the horizontal

when there is air resistance

let the initial speed of ball be u

range = 60 yards = 54.86 m

u^2 * sin(2*theta) /g = 54.86

u^2 * ( sin(2 * 45)) /9.81 = 54.86

solving for u

u = 23.2 m/s

when there is air resistance

the time of flight , t = 2 * u * sin(45)/9.81

t = 2 * 23.2 * sin(45) /9.81 s

t = 3.34 s

the new range , R' = u * cos(45) * t - 0.5 * ax * t^2

R' = 23.2 * 3.34 * cos(45)- 0.5 * 3 * 3.34^2

R' = 38 m = 41.6 yards

so, he will not be able to go for that kick