Question 9.51: In Fig. 9-58a, a 3.50 g bullet is fired horizontally at two ......
In Fig. 9-58a, a 3.50 g bullet is fired horizontally at two blocks at rest on a frictionless table. The bullet passes through block 1 (mass 1.20 kg) and embeds itself in block 2 (mass 1.80 kg). The blocks end up with speeds \nu_{1} = 0.630 m/s and \nu_{2}\, = 1.40 m/s (Fig. 9-58b). Neglecting the material removed from block 1 by the bullet, find the speed of the bullet as it (a) leaves and (b) enters block 1.
In solving this problem, our +x direction is to the right (so all velocities are positive-valued).
(a) We apply momentum conservation to relate the situation just before the bullet strikes the second block to the situation where the bullet is embedded within the block.
(0.0035\mathrm{\ kg})\nu=(1.8035\mathrm{\ kg})(1.4\mathrm{\ m/s})\ \Longrightarrow\ \nu=721\ \mathrm{m/s}.
(b) We apply momentum conservation to relate the situation just before the bullet strikes the first block to the instant it has passed through it (having speed ν found in part (a)).
(0.0035\mathrm{\ kg})\nu_{0}=(1.20\mathrm{\ kg})(0.630\mathrm{\ m/s})+(0.00350\mathrm{\ kg})(721\mathrm{\ m/s})
which yields \nu_{0}=937\,\mathrm{m/s}.