Answer to Question #101852 in Mechanics | Relativity for zs

Question

Two astronauts are facing off in a fight outside the International space station. Astronaut Pitt (78 kg) and astronaut Reeve (80 kg) are initially at rest with respect to each other. Pitt pushes Reeve hard towards the earth at a speed of 3 m/s. Ignoring friction,
a) What is the velocity of Pitt after the push?

b) What is the minimum amount of chemical energy that is converted into mechanical energy in Pitt’s muscles from his action?

Answer 1

a) From the conservation of momentum:

$$m_Pv_P=m_Rv_R$$

$$(80)(3)=(78)v_P$$

$$v_P=3.08\frac{m}{s}$$

Directed from the Earth.

b)

$$E=K=0.5(m_pv_p^2+m_Rv_R^2)$$

$$E=0.5((78)(3.08)^2+(80)(3)^2)=730\ J$$