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 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. **Please show Work, Im looking to understand it more so then aquire the answer, thanks

Explanation / Answer

time taken for arrow to reach target mv^2=kx^2 elastic energy of spring is equal to kinetic energy of arrow 0.05*v^2=600*0.5^2 v^2=3000 v=54.77 t=x/v=20/54.77=0.3651 the vertical distance travelled by arrow in this time due to gravity=1/2*a*t^2=0.5*9.81*0.3651^2=0.6539m the vertical height by which it undershoots is 65cm

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