Guide To Archery

Rest Bow

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An arrow, starting from rest, leaves the bow with a speed of 14.5 m/s.?

An arrow, starting from rest, leaves the bow with a speed of 14.5 m/s. If the average force exerted on the arrow by the bow were doubled, all else remaining the same, with what speed would the arrow leave the bow?
(sig figs please~:D)

Let us assume force applied in first case is F and speed in second case is V.
Since the bow will only accelerate the arrow through a fixed distance (let's say d), work done on arrow in first case ( = kinetic energy of arrow) is F * d.

When force is 2F, work done is 2F * d.

Ratio of arrow's kinetic energy in the 2 cases is 1 : 2, i.e.

(14.5 m/s)^2 : V^2 :: 1 : 2, ( since KE = 1/2 * m * v^2 )

thus, V^2 = 2 * (14.5 m/s)^2

thus, V = 20.5 m/s.

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An arrow, starting from rest, leaves the bow with a speed of 14.5 m/s.?

An arrow, starting from rest, leaves the bow with a speed of 14.5 m/s. If the average force exerted on the arrow by the bow were doubled, all else remaining the same, with what speed would the arrow leave the bow?
(sig figs please~:D)

Let us assume force applied in first case is F and speed in second case is V.
Since the bow will only accelerate the arrow through a fixed distance (let's say d), work done on arrow in first case ( = kinetic energy of arrow) is F * d.

When force is 2F, work done is 2F * d.

Ratio of arrow's kinetic energy in the 2 cases is 1 : 2, i.e.

(14.5 m/s)^2 : V^2 :: 1 : 2, ( since KE = 1/2 * m * v^2 )

thus, V^2 = 2 * (14.5 m/s)^2

thus, V = 20.5 m/s.

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