A football kicker can give the ball an initial speed of30 m/s. He is 32m from th

Question

A football kicker can give the ball an initial speed of30 m/s. He is 32m from the goalpost which has a crossbar 3.50 m high. (a) What is the smallest angle of elevationthat he can kick the football and score a field goal?
1°

(b) What is the largest angle of elevation that he can kick thefootball and score a field goal?
2° (a) What is the smallest angle of elevationthat he can kick the football and score a field goal?
1°

(b) What is the largest angle of elevation that he can kick thefootball and score a field goal?
2°

Explanation / Answer

theangle of elevation that he can kick the football and scorea field goal is the equation of motion y(t)= 30*sin*t -g*t2/2 x(t)=30*cos*t => y(t)=x(t)*tan -g*x(t)2/2*v2*(1+tan2) (a) min <=> x(t)=32 m ; y(t)=0 plug the values => tan=0.1799 =>=10.20 (b) max <=> x(t)=32 m; y(t) =3.5 m => tan =5.44 =>=79.60 the equation of motion y(t)= 30*sin*t -g*t2/2 x(t)=30*cos*t => y(t)=x(t)*tan -g*x(t)2/2*v2*(1+tan2) (a) min <=> x(t)=32 m ; y(t)=0 plug the values => tan=0.1799 =>=10.20 (b) max <=> x(t)=32 m; y(t) =3.5 m => tan =5.44 =>=79.60

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