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AP Physics C: Mechanics/Unit 4 – Linear Momentum
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Variable-Mass Rocket Momentum

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A rocket with an initial mass of m0m_0 starts from rest. It ejects gas at a constant rate given by dmdt=−k\frac{dm}{dt} = -k and at a constant velocity u⃗=−ui^\vec{u} = -u\hat{i} relative to the rocket. In the absence of external forces, what is the magnitude of the rocket’s momentum at time tt?

A

ku(m0−kt)ku(m_{0} - kt)

B

kutkut

C

m0u(1−e−kt/m0)m_{0}u(1 - e^{-kt/m_{0}})

D

u(m0−kt)ln⁡(m0m0−kt)u(m_{0} - kt)\ln\left(\frac{m_{0}}{m_{0} - kt}\right)

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