Question

body? Answer in symbols, numbers and numbers of body weight (i.e. find F/mg) , P2 Use b same swers 9.2.11 In traditional archery, when pulling Whyn an arrow back the force starts from 0 and increases approximately linearly up to the peak draw force' Fdrau The draw force varies from about Fdra u' 一25 lbf for agree, right? a bow made for a small person to about 9.2.14 Fdraw = 75 lbf for a bow made for a big would strong person. The distance the arrow is deceler pulled back, the draw length (dra variesing the from about d raw 2 ft for a small adult would b = 2 ft for a small adult would E to about 30inch for a big adult. An ar same, f on the n row has mass of about 300 grain (1 grain 64.8mil lien. so an arrow has mass of about 19.44 20gm3/4 ounce). Give tion? all answers in symbols and numbers. a) What is the range of speeds you can 9,2.15 T expect an arrow to fly? b) What is the range of heights an ar mayst row might go if shot straight up (it's ll at t a bad approximation. but for this the radiu tic rocket velocity c problem neglect air friction)? rotating-W the rocket the earth tu 10kg) jumpssurface of

Answer 1

(a) Force divided by mass gives acceleration. So a= F/m. Now initial velocity u=0 and final velocity is v, and the force is acted upon for a distance S = l_draw .So we have

$v^2 = u^2 + 2aS \Rightarrow v = \sqrt{2\frac{F}{m}l_{draw} }$

here mass is fixed which is 3/4 ounces = 0.046875 pounds

for small adult

$v = \sqrt{2\frac{25}{0.046875}2 } = 46.188\ ft/s = 14.078\ m/s$

for large adult

l_draw = 30 inches = 2.5 ft

$v = \sqrt{2\frac{75}{0.046875}2.5 } = 89.443\ ft/s = 27.262\ m/s$

(b) In upward motion, the maximum height reached H is given by

$H = \frac{v^2}{2g}$

for small adult

$H = \frac{(14.078\ m/s)^2}{2\times 9.8\ m/s^2} = 10.112\ m = 33.175 ft$

for large adult

$H = \frac{( 27.262\ m/s)^2}{2\times 9.8\ m/s^2} = 37.919\ m = 124.407 ft$