An archer stands on a cliff with his bow 32.5 meters above a valley and fires an

Question

An archer stands on a cliff with his bow 32.5 meters above a valley and fires an arrow with a mass of 35.1 grams straight upward.

a. If the bow has an average “pull strength” of 131 N and the arrow travels 0.762 m (the “draw length”) before it leaves the bow, how much work does the bowstring do on the arrow?
b. How much kinetic energy does the arrow have when it leaves the bow?How fast is it going?
c. The arrow goes straight up, and since air resistance and wind can be neglected today, comes straight back down and lands in the valley below. Draw a diagram for its motion, and create formulas for the kinetic energy and potential energy of the arrow at three points: when it leaves the bow, at the peak of its motion, and when it hits the ground in the valley.
d. Use energy methods to find how high the arrow gets.
e. Use energy methods to find the speed of the arrow when it hits the ground.

Explanation / Answer

a) m = 0.0351 kg

work = FOrce* distance = 131*0.762 m = 99.822 Nm

b) Kinetic energy = work done = 99.82 Nm = 1/2 mV^2 thus V = 75.41m/s

c)

d) mgh1 + kinetic energy = mgH2

111 = mgH2

H2 = 322.39m

e)mgH2 = 1/2m*V2

111 = 1/2mV^2

V = 79.52m/s

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