What is the speed of Earth toward the bag just before the bag hits the ground?

Question

A 7.33 kg laundry bag is dropped from rest at an initial height of 4.57 m. The acceleration of gravity is −9.81 m/s 2. Use the value 5.98 × 1024 kg as the mass of Earth. What is the speed of Earth toward the bag just before the bag hits the ground? Answer in units of m/s.

Answer 1

The magnitudes of the gravitational forces between Earth and the bag are equal, |F_g| = |M_E a_E| = |m_b g|, so a_E = (7.33 kg) (9.81 m/s²) / (5.98 x 10²⁴ kg) = +1.20₂ x 10^-23 m/s².

Δy = v_o t + 1/2 a t², -4.57 = 0 - (9.81/2) t², t² = 0.931₇ and t = 0.965₂ s.

v_E = v_o + a_E t = 0 + 1.16 x 10^-23 m/s.