Answer:
For the ball to travel the greatest distance it must be kicked at an angle of 45° to the horizontal
Since 90° is upward 0° is straightforward 45° splits at the middle to give the greatest distance
Explanation:
What is the maximum range of a projectile?
The range (R) of the projectile is the horizontal distance it travels during the motion.
The reason that 45 degrees is the best launch angle (resulting in the longest flight) is that it perfectly splits the upward and forward forces. Ninety degrees is straight up. Zero degrees is straight forward. 45 degrees is right in the middle, half of 90.
The angle that makes the highest horizontal distance is required.
The maximum range will be 40.77 m at an angle of [tex]45^{\circ}[/tex]
u = Initial velocity = 20 m/s
g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]
The horizontal range is given by
[tex]x=\dfrac{u^2}{g}\sin2\theta[/tex]
The value of [tex]\sin \theta[/tex] ranges from [tex]-1[/tex] to [tex]1[/tex].
So, range will be maximum when
[tex]\sin 2\theta=1\\\Rightarrow 2\theta=\sin^{-1}1\\\Rightarrow 2\theta=90^{\circ}\\\Rightarrow \theta=\dfrac{90}{2}\\\Rightarrow \theta=45^{\circ}[/tex]
[tex]x=\dfrac{20^2}{9.81}\sin(2\times 45)\\\Rightarrow x=40.77\ \text{m}[/tex]
The maximum range will be 40.77 m at an angle of [tex]45^{\circ}[/tex]
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