# For tests using a ballistocardiograph, a patient lies on a horizontal platform that is supported on jets of air. Because of the air jets, the friction

For tests using a ballistocardiograph, a patient lies on a horizontal platform that is supported on jets of air. Because of the air jets, the friction impeding the horizontal motion of the platform is negligible. Each time the heart beats, blood is pushed out of the heart in a direction that is nearly parallel to the platform. Since momentum must be conserved, the body and the platform recoil, and this recoil can be detected to provide information about the heart. For each beat, suppose that 0.050 kg of blood is pushed out of the heart with a velocity of +0.30 m/s and that the mass of the patient and the platform is 85 kg. Assuming that the patient does not slip with respect to the platform, and that the patient and the platform start from rest, determine the recoil velocity.
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tabuordg
given for blood mass
initial velocity
final velocity
for man mass
initial velocity is ${v}_{o2}$ final velocity
applying principle of conservation of linear momentum we have
${m}_{1}{v}_{01}+{m}_{2}{v}_{02}={m}_{1}{v}_{f1}+{m}_{2}{v}_{f2}$
Or ${v}_{o2}=-\left(\frac{{m}_{1}}{{m}_{2}}\right)\cdot {v}_{o1}$