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https://texercises.com/exercise/william-tell/
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Exercise:
William Tell must split the apple atop his son's head from a distance of m. When William aims directly at the apple the arrow is horizontal. At what angle must he aim it to hit the apple if the arrow travels at a speed of meterpersecond?

Solution:
The question we have to answer is: At what angle is the maximum width m concerning meterpersecond? As in every ballistic-exercise the vertical motion determines the time of the motion. The arrow will travel for t t_uparrow + t_downarrow t_uparrow fracv_yg fracv_sinalphag Knowing that the width the arrow reaches at any angle alpha is: s_x v_x t v_cosalpha fracv_sinalphag fracv_^gsinalpha Here we used sinalphacosalpha frac sin alpha. We can solve this last for the angle alpha: alpha frac arcsinleft fracgs_xv_^ right ang.
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Exercise:
William Tell must split the apple atop his son's head from a distance of m. When William aims directly at the apple the arrow is horizontal. At what angle must he aim it to hit the apple if the arrow travels at a speed of meterpersecond?

Solution:
The question we have to answer is: At what angle is the maximum width m concerning meterpersecond? As in every ballistic-exercise the vertical motion determines the time of the motion. The arrow will travel for t t_uparrow + t_downarrow t_uparrow fracv_yg fracv_sinalphag Knowing that the width the arrow reaches at any angle alpha is: s_x v_x t v_cosalpha fracv_sinalphag fracv_^gsinalpha Here we used sinalphacosalpha frac sin alpha. We can solve this last for the angle alpha: alpha frac arcsinleft fracgs_xv_^ right ang.
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Tags
mechanics, physics, tell, throw, trajectory, william
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Difficulty
(2, default)
Points
5 (default)
Language
ENG (English)
Type
Calculative / Quantity
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Link