You are on an iceboat on frictionless, flat ice; you and the boat have a combine

Question

You are on an iceboat on frictionless, flat ice; you and the boat have a combined mass M. Along with you are two stones with masses m1 and m2 such that M = 6.0000m1 =12.000m2. To get the boat moving, you throw the stones rearward, either in succession or together, but in each case with a certain speed 15.000 m/s relative to the boat. What is the resulting speed of the boat if you throw the stones simultaneously?

What is the resulting speed of the boat if you throw the stones m1 and then m2?

What is the resulting speed of the boat if you throw the stones m2 and then m1?

Explanation / Answer

(b)Apply conservation of momentum

(M + m2) vM -m1v1=0

then   vM= m1v1 /(M + m2 )
vM = m1 15 /(6.00m1 + 0.5m1)
vM = 15/ 6.5= 2.30 m/s
then we repeat for m2
(M+   m2 ) vM - M v'M    - m2v2 =0
vM' =[(m2v2 + (M+   m2 ) vM] / M
vM' = [(0.5m1 15+ (6m1+   0.5m1) 2.3] / 6m1

vM' =3.74 m/s

----------------------------------------------------------------------------------------------------------------------------------------

M vM - (m1+ m2 ) v1=0
vM = [(m1 + m2 ) / M ] v1
vM= [(2m2 + m2 ) / 12m2] 15
vM = [(3 ) / 12 ] 15 =3.74 m/s

(a) both have same speed

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