Question

A football is launched at 40 m/s, at an angle from the ground. What should the angle be such that maximum height of the trajectory of the football is 10 m?

Answer 1

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:

$v_{i}$: total initial speed  =$40\frac{m}{s}$

$v_{iy}$:initial speed component in vertical direction (y) =$v_{i} sin\alpha$

$v_{y}$: vertical speed at any point on the parabolic path

g= acceleration of gravity= 9,8 $\frac{m}{s^{2} }$

$\alpha$= angle that forms the total initial velocity with the ground

Equation of the speed of the football in the vertical direction :

$(v_{y} )^{2}=(v_{iy} )^{2} -2*g*y$  Equation (1)  

We replace$v_{iy} =40*sin\alpha$, $g=9.8\frac{m}{s^{2} }$  in the equation (1):

$(v_{y} )^{2} =(40*sin\alpha )^{2} -2*9.8*y$ 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$v_{y} =0$ , $y=10$ in the equation (2)

$0=(40*sin\alpha )^{2} -2*9.8*10$

$0=1600*(sin\alpha )^{2} -196$

$\frac{196}{1600} =(sen\alpha )^{2}$

$0.1225=(sin\alpha )^{2}$

$\sqrt{0.1225} =sin\alpha$

$0.35=sin\alpha$

$\alpha =20.487$ °

Answer:The football must be launched whit an angle of 20,487 degrees to reach a maximum height of 10 meters.