Answer:
v = -0.938 m/s ( the negative sign indicating the direction of the cart is opposite the motion of Ethan)
Explanation:
mass of Ethan (Me) = 67 kg
mass of cart (Mc) = 500 kg
Ethan's top speed (Ts) = 8 m/s
let the velocity of the cart be v
relative to the earth, Ethan will be moving forward while the cart will be moving backward, therefore
Ethan,s velocity relative to the earth = 8 -v,
apply the conservation of momentum equation
MeUe + McUc = MeVe + McVc
where Ue and Uc are the initial velocities of Ethan and the cart and are all zero, the left side of the equation is equal to zero
0 = MeVe + McVc
0 = (67 x (8-v)) + (500 x v)
0 = 536v - 67v + 500v
0 = 469 + 500v
v = -469/500
v = -0.938 m/s ( the negative sign indicating the direction of the cart is opposite the motion of Ethan)
