Question

1) A cardinal (*Richmondena cardinalis*) of mass
4.20×10^{−2} kg and a baseball of mass 0.140 kg have the
same kinetic energy. What is the ratio of the cardinal's magnitude
*p*c of momentum to the magnitude *p*b of the
baseball's momentum?

2) A man weighing 750 N and a woman weighing 460 N have the same
momentum. What is the ratio of the man's kinetic energy *K*m
to that of the woman *K*w?

Answer #1

**1)** Mc,Vc = cardinal's mass and velocity

Mb,Vb = baseball's mass and velocity

(Mc)(Vc)² = (Mb)(Vb)²

(Mc)/(Mb) = (Vb/Vc)²

(Vb/Vc) = √(Mc/Mb)

(McVc)(Vc) = (MbVb)(Vb)

(McVc)/(MbVb) = (Vb/Vc) = √(Mc/Mb) = √(.042/0.140) ≈ 0.548

**The cardinal's momentum is approximately 0.548 of the
baseball's momentum**

**2)** mass x vel = momentum

750 x Vm = 460 x Vw

Vm = 460/750 x Vw

Km = 0.5 x 750 x [460/750 Vw]^2 = 0.5 x 460^2/750 x Vw^2

Kw = 0.5 x 460 x Vw^2

**Km/Kw = 460/750 = 0.613 to 1**

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