Particles $$$P$$$ of mass $$$0.4 \mathrm{~kg}$$$ and $$$Q$$$ of mass $$$0.5 \mathrm{~kg}$$$ are free to move on a smooth horizontal plane. $$$P$$$ and $$$Q$$$ are moving directly towards each other with speeds $$$2.5 \mathrm{~m} \mathrm{~s}^{-1}$$$ and $$$1.5 \mathrm{~m} \mathrm{~s}^{-1}$$$ respectively. After $$$P$$$ and $$$Q$$$ collide, the speed of $$$Q$$$ is twice the speed of $$$P$$$. Find the two possible values of the speed of $$$P$$$ after the collision. ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_43 Year：2021 Question No：1

Answer:

$ \begin{array}{l}
0.4 \times 2.5-0.5 \times 1.5 \\
0.4 \times 2.5-0.5 \times 1.5=0.4 v+0.5 \times 2 v \\
0.4 \times 2.5-0.5 \times 1.5=0.4 v+0.5 \times 2 v \\
\text { or } 0.4 \times 2.5-0.5 \times 1.5=-0.4 v+0.5 \times 2 v
\end{array}
$
Speed is $0.179 \mathrm{~m} \mathrm{~s}^{-1}$ or $0.417 \mathrm{~m} \mathrm{~s}^{-1}$

Knowledge points:

4.3.2 use conservation of linear momentum to solve problems that may be modelled as the direct impact of two bodies. （Including direct impact of two bodies where the bodies coalesce on impact. Knowledge of impulse and the coefficient of restitution is not required.）

Answer:

Knowledge points:

Solution:

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