You are watching people practicing archery when you wonder how fast an arrow is

Question

You are watching people practicing archery when you wonder how fast an arrow is shot from a bow. Remembering your physics, you realise that you can figure this out with a simple measurement. You ask one of the archers to pull back the bowstring as far as possible and shoot an arrow horizontally. The arrow strikes the ground at an angle of =4° below the horizontal, at distance L= 140.0 ft from the archer. Find the initial speed vi that an arrow must have to cover this distance.

need answer in ft/s

Explanation / Answer

Let the intital velocity be u

Using the equation of motion,

v = u + at

In vertical direction,

vy = 0 +9.8*t = 9.8*t

In horizontal direction,

vx = u

So, tan(4 deg) = 9.8*t/u ------(1)

In horizontal direction,

L = u*t = 140

So, t = 140/u

So, tan(4 deg) = 9.8*140/u^2

So, u = 140.1 m/s = 459.3 ft/s <-------answer

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