An archer is shooting an arrow at a stationary target 20 m away. Assume that the

Question

An archer is shooting an arrow at a stationary target 20 m away. Assume that the mass of the arrow is about 50 g and that the bow can be treated as an elastic spring with spring constant k = 600 N/m. The archer stretches the bowstring over distance of approximately 50 cm. He aims directly at the target and as a result the arrow is released strictly horizontally. What is the vertical amount ?y by which the arrow will undershoot the target due to the action of gravity? This shows you that one must aim the arrow slightly at an angle, instead of launching it horizontally. Ignore the presence of air resistance. Can you please provide me the solution with the formulas?

Explanation / Answer

initial velocity of arrow (v) 0.5 x 300 x 0.5^2 = 0.5 x 0.05 x v^2 v = 54.77 m/s time to reach target = 20 / 54.77 = 0.365 s undershoot of the arrow = 0.5 x 9.8 x 0.365^2 = 0.65 m = 65 cm

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