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

(a)the smallest angle of elevation that he can kick thefootball and score a field goal (just enough to reach the distaceof 32m) we know that distance L=v2*sin2/g , with v is initialspeed of the object =>32=302*sin2/9.8 =>=10.20   (b)the largest angle of elevation thathe can kick the football and score a field goal it means the ball smashs on thecrossbar equation of motion y(t)=30*sin*t -g*t2/2(1) x(t)=30*cos*t with x(t)=32 m=>t=16/15cos subs to (1) : 3.5=32*tan-g*128/225*(1+tan2) => tan=5.441(we need the max value) =>=79.590 equation of motion y(t)=30*sin*t -g*t2/2(1) x(t)=30*cos*t with x(t)=32 m=>t=16/15cos subs to (1) : 3.5=32*tan-g*128/225*(1+tan2) => tan=5.441(we need the max value) =>=79.590

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