When a field goal kicker kicks a football as hard as he can at 45° to the orizon

Question

When a field goal kicker kicks a football as hard as he can at 45° to the orizontal, the ball just clears the 3 m high (a) What is the maximum speed (in m/s) the kicker can impart to the footbal? mýs In addition to clearing the crossbar, the footbal must be high enough in the air early dring its Nght to dear the reach ofthe onshing deener Ineran r-re a vertical reach of 2.6 m, can he block the 40.4 m field goal attempt? (b) Yes, he can block the field goal attempt at this distance. No, he cannot block the field goal attempt at this distance. (c) What if the lineman is 4.3 m away? Yes, he can block the field goal attempt at this distance O No, he cannot block the field goal attempt at this distance

Explanation / Answer

a] maximum height H = u^2 [ sin 45 degree]^2/2g  

3 = u^2 *0.5/(9.8*2)

u = sqrt(3*2*9.8/0.5)

= 10.844 m/s

b] time taken to pass him, t=1.4/[10.844 cos 45 degree] = 0.1826 s

vertical height of the ball = 10.844*sin 45 degree*0.1826^2 - 0.5*9.8*0.1826^2

= 0.0923 m < 2.6 m

hence he can block the ball, t =4.3/[10.844 cos 45 degree] = 0.56078 s

height of ball = 10.844* sin 45 degree*0.56078 - 4.9*0.56078^2

= 2.76m > 2.6m

Hence he can not block the ball

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