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A 6.00 times ten to the seventh kg battleship, initially at rest, fires a 1100 kg shell horizontally at 575 m/s straight aft, with negligible friction opposing the recoil. What is the battleship's recoil speed?
AAbout 0.000105 m/s
BAbout 1.05 m/s
CAbout 10.5 m/s
DAbout 0.0105 m/s
Answer & Solution
Correct answer: D. About 0.0105 m/s
1. Before firing, the total momentum of the battleship and shell system is zero, since both start at rest.
2. Momentum conservation requires the battleship's momentum after firing to be equal and opposite to the shell's momentum.
3. The shell's momentum is (1100 kg)(575 m/s), which is 632500 kg m/s.
4. Dividing by the battleship's mass of 6.00 times ten to the seventh kg gives a recoil speed of about 0.0105 m/s, in the direction opposite the shell.
5. The other options are each off from this value by one or more factors of ten.
_Source: OpenStax College Physics (CC BY 4.0), Ch 8 "Linear Momentum and Collisions", section 8.5 Inelastic Collisions in One Dimension_
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