Example 9.1The Archer ( I just need help on the bolded part at the end) A 70-kg

Question

Example 9.1The Archer ( I just need help on the bolded part at the end)

A 70-kg archer stands at rest on frictionless ice and fires a 0.050-kg arrow horizontally at 54 m/s (see the figure). With what velocity does the archer move across the ice after firing the arrow?

What if he misses the target, and pulls out a second arrow (of the same weight as the first) to fire again? This time, he fires it harder. The arrow is measured to have a velocity of 67 m/s by a stationary bystander. This happens while the archer is still sliding backwards at

?0.039 m/s.

What will be his velocity (in the xdirection) after firing the second arrow? (Notice that his "mass" after firing the second arrow will be 69.900 kg!)
m/s

An archer fires an arrow horizontally to the right. Because he is standing on frictionless ice, he will begin to slide to the left across the ice.

Explanation / Answer

For the bolded part,

Initial velo. of archer plus second arrow, u1 = -0.039m/s
Initial mass of archer plus second arrow, m1 = 69.950 kg

Final velo. of arche, v1 = ?
Final velo. of arrow, v2 = 67m/s
mass of archer after firing 2nd arrow, m = 69.900kg
mass of 2nd arrow, m0 = 0.050kg

By conservation of momentum,

m1u1 = mv1 + m0v2
69.950 x (-0.039) = 69.900 x v1 + 0.050 x 67
69.900 x v1 = 69.950 x (-0.039) - 0.050 x 67
v1 = - 0.086m/s

So, he moves backward with  0.086m/s after firing 2nd arrow

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