The Speed and Angle of an Arrow Shot from a Longbow

このQ&Aのポイント
  • Learn how to estimate the speed and angle at which an arrow must leave a longbow to reach a target 100 meters away, given a maximum altitude of 20 meters and neglecting air resistance.
  • Plot the required release speed and angle as a function of the arrow's maximum altitude while traveling to the target.
  • Discover the accuracy and range of longbow arrows, which can reach targets up to 100 meters or more.
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この問題の解き方を教えてください。

The longbow are acurate at ranges to 100 meters or more. If the maximum altitude of an arrow is less than h = 20m while travelling to a target 100 m away from the archer, and neglecting air resistance, esitimate the speed and angle at which the arrow must leave the bow. plot the required release speed and angle as a function of height h

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回答No.2

矢の水平方向の運動エネルギーはへんかなしですね。 > 垂直方向の運動エネルギーは、20m上空で0になります。 これで矢を放つときの垂直方向の運動エネルギーは決定されます。 > 最初の垂直方向の運動エネルギーから速度も求まります。 ただし、矢の質量が記されていませんので、仮に1kgとします。 > 初速度が求まれば、20m上空まで達する時間も求まります。 その間に水平方向に50m進むわけです。

primula2
質問者

補足

回答ありがとうございました。 アドバイスにしたがってといてみましたけどこれでよいのでしょうか。 E=KE + PE = (1/2)mv^2 + mgh  ///  KE:kinentic energy, PE: poential enenrgy Using the conservation of energy, (1/2) mv0y^2 = mgh, and v0y = (2gh)^(1/2) /// v0y: Y component of intitial V vy = v0y – gt, /// vy: Y component of V At the maximum h, vy= 0, 0 = v0y – gt = (2gh)^(1/2) – gt, and t = (2gh)^(1/2)/ g x= v0xt, and v0x = x/t /// v0x: x component of intitial V Substituting x = 50, and t = (2gh)^(1/2)/ g v0x = (50)g/(2gh)^(1/2) Tanθ= v0y/v0x, and θ = Arctan(v0y/v0x)= Arctan((2gh)^(1/2)/((50)g/(2gh)^(1/2)) = Arctan(h/25) v0 = (v0x^2+v0y^2)^(1/2) = (1250g/h + 2gh)^(1/2) Substituting h = 20 and g = 9.81, θ = Arctan(h/25) = Arctan(20/25) = 38.7 degree v0 = (1250g/h + 2gh)^(1/2) =((1250)(9.81)/20 + 2(9.81)(20))^(1/2) = 31.7m/s もしまちがっていればご指摘ください。

その他の回答 (2)

回答No.3

>plot the required release speed and angle as a function of height h 英文を正確に読むと、h=20mで解くわけでないようです。 初期スピードと角度をhの関数で表現するようです。 でも、できているようです。

  • okormazd
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回答No.1

acurate→accurate ? esitimate→estimate ? plot→Plot ? height h→height h. ? 英文の意味は解るのですか。

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