(a)p = mv, with mass converted to kg (58 g = 0.058 kg).

(a)Total momentum before = total momentum after: m1u1 + m2u2 = (m1+m2)v.

(b)Conservation of momentum: in a closed system with no external forces, total momentum before a collision equals total momentum after.

(a)Take the initial direction as positive, so the rebound velocity is −6.0 m/s. Δp = m(v − u).

(b)F = Δp / Δt.

(a)Total momentum before pushing off is zero (both at rest). By conservation of momentum, total momentum must still be zero afterward, so the skaters' momenta must be equal and opposite — meaning they move in opposite directions.

(a)p = mv.

(a)F = Δp/Δt = m(v−u)/t.

(a)Total momentum before = total momentum after: m1u1 + m2u2 = (m1+m2)v, taking the 2kg trolley's velocity as −1 m/s.

(a)Total momentum starts at zero, so the astronaut's momentum must be equal and opposite to the tool's: m_astro × v_astro = −m_tool × v_tool.

(a)In a closed system with no external forces, the total momentum before an interaction equals the total momentum after it.

(a)Padding increases the time over which the impact momentum change happens. Since F = Δp/Δt, a longer contact time for the same change in momentum results in a smaller average force on the person hit.