Answer:
The football must be launched whit an angle of 20,487 degrees to reach a maximum height of 10 meters.
Explanation:
To solve this problem we use the parabolic motion equations:
We define:
[tex]v_{i}[/tex]: total initial speed =[tex]40\frac{m}{s}[/tex]
[tex]v_{iy}[/tex]:initial speed component in vertical direction (y) =[tex]v_{i} sin\alpha[/tex]
[tex]v_{y}[/tex]: vertical speed at any point on the parabolic path
g= acceleration of gravity= 9,8 [tex]\frac{m}{s^{2} }[/tex]
[tex]\alpha[/tex]= angle that forms the total initial velocity with the ground
Equation of the speed of the football in the vertical direction :
[tex](v_{y} )^{2}=(v_{iy} )^{2} -2*g*y[/tex] Equation (1)
We replace[tex]v_{iy} =40*sin\alpha[/tex], [tex]g=9.8\frac{m}{s^{2} }[/tex] in the equation (1):
[tex](v_{y} )^{2} =(40*sin\alpha )^{2} -2*9.8*y[/tex] Equation(2)
Angle calculation
The speed of the football in the vertical direction gradually decreases until its value is zero when it reaches the maximum height.
We replace[tex]v_{y} =0[/tex] , [tex]y=10[/tex] in the equation (2)
[tex]0=(40*sin\alpha )^{2} -2*9.8*10[/tex]
[tex]0=1600*(sin\alpha )^{2} -196[/tex]
[tex]\frac{196}{1600} =(sen\alpha )^{2}[/tex]
[tex]0.1225=(sin\alpha )^{2}[/tex]
[tex]\sqrt{0.1225} =sin\alpha[/tex]
[tex]0.35=sin\alpha[/tex]
[tex]\alpha =20.487[/tex] °
Answer:The football must be launched whit an angle of 20,487 degrees to reach a maximum height of 10 meters.
