Bow and Arrow.? Figure shows how the force exerted by the string of a compound bow on an arrow varies as a function of how far back the arrow is pulled (the draw length). Assume that the same force is exerted on the arrow as it moves forward after being released. Full draw for this bow is at a draw length of 75.0 cm. If the bow shoots a 0.0250-kg arrow from full draw, what is the speed of the arrow as it leaves the bow? Figure:

Solution 88P Step 1 of 1 According to work energy theorem, work done = change in kinetic energy W total (K.E) 2(K.E) 1 X varies from x=0 to x=x , 0 4 F F(x) = ( 20)x(x 0 x) 0 x 0 4F0 2 F dx = x (x0x x )dx x 0 2 3 4F 0 x0 x0 = x2 (x 0 2 2 ) 0 2 = 3 x0 0 v = 2W The speed of the arrow is, m 2×100 J = 0.025 kg = 89 m/s