## Physics: Principles with Applications (7th Edition)

(a) $m_cv_c = m_av_a$ $v_c = \frac{m_av_a}{m_c}$ $v_c = \frac{(125 ~kg)(2.50 ~m/s)}{(1900 ~kg)}$ $v_c = 0.164 ~m/s$ The change in speed of a the space capsule is 0.164 m/s. (b) $F\times t = \Delta p$ $F\times t = m_av_a$ $F = \frac{m_av_a}{t}$ $F = \frac{(125 ~kg)(2.50 ~m/s)}{(0.600 ~s)}$ $F = 521 ~N$ The average force that the astronaut and the space capsule exert on each other is 521 N. (c) $KE_a = \frac{1}{2}(125 ~kg)(2.50 ~m/s)^2$ $KE_a = 391 ~J$ $KE_c = \frac{1}{2}(1900 ~kg)(0.164 ~m/s)^2$ $KE_c = 25.6 ~J$ The kinetic energy of the astronaut is 391 J and the kinetic energy of the space capsule is 25.6 J.