William Tell must split the apple atop his son’s head from

William Tell must split the apple atop his son's head from a distance of 28.0 m. When he 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 31.8 m/s?

2 Answers

  • Since the arrow and apple are at the same height, use the range equation:

    x = V²sin(2Θ) / g

    28.0 m = (31.8m/s)²sin(2Θ) / 9.8m/s²

    sin(2Θ) = 0.271

    2Θ = 15.7º

    Θ = 7.87º

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  • When the arrow moves through the air it is pulled down by the gravity. This should be corrected. Let v be the horizontal velocity. The time taken by the arrow to reach 28 m is 28/v. In this it falls through the distance

    s = 1/2 g t^2= 1/2 g (28/v)^2.

    s and horizontal direction make a right angled triangle. Therefore, the angle theta must be

    tan theta = g/2 28^2/v^2 /28

    Put the values

    tan theta=0.136

    theta= 7.745 degrees above the horizontal direction.

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