Robin Hood is walking through Sherwood Forest when he comes upon the Sheriff of

Question

Robin Hood is walking through Sherwood Forest when he comes upon the Sheriff of Nottingham. The Sheriff tells Robin Hood that he is going to arrest him for numerous misdeeds. Robin pulls out his bow, loads an arrow, pulls the bow back 0.70 m, and shoots an arrow into the Sheriff’s hat, knocking the hat with the arrow lodged in it off his head. The hat’s mass is 0.5 kg. It takes 4 N to pull Robin’s bow back 0.10 m, and the arrow has a mass of 0.20 kg.

A) What is the speed of the hat with the arrow in it just after it is struck? Assume the arrow travels horizontally between Robin and the Sheriff and neglect air resistance. (Answer should be around 2.8 m/s)

B) If the Sheriff is 2.0 m high, how far behind him will his hat with the arrow in it hit the ground?

Explanation / Answer

force constant of bow = k = F/x = 4/0.1 = 40 N/m

energy stored in bow = U = 0.5*k*A^2

kinetic energy of arrow = KE = 0.5*m*v1^2

from energy conservation

U = K

0.5*40*0.7^2 = 0.5*0.2*v1^2

v1 = 9.9 m/s

after collision

momentum before collision = momentum after collision

m1*v1 = (m1+m2)*V

V = (0.2*9.9)/(0.2+0.5)

v = 2.8 m/s <<----answer

+++++++++

along vertical

h = 0.5*g*T^2

T = sqrt(2h/g)

along horizantal

x = v*T = 2.8*sqrt(2*2/9.8) = 1.8 m <<-------answer

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