# A compact car, mass 650 kg, is moving at 100 km/hr toward the south. How do you find the magnitude and direction of its momentum? A second car, with a mass of 2175 kg, has the opposite momentum. What is its velocity?

Feb 6, 2017

Let East direction be $+ x$-axis and North direction be $+ y$-axis.
Velocity of compact car of mass $m = - 100 \hat{y} {\text{ kmh}}^{-} 1$

Converting in SI units we get
Velocity of compact car$= - 100 \times \frac{1000}{3600} \hat{y} {\text{ ms}}^{-} 1$
$= . - \frac{1000}{36} \hat{y} {\text{ ms}}^{-} 1$

Momentum $\vec{p} = m \vec{v}$
Inserting values we get
Momentum $\vec{p} = 650 \times \left(- \frac{1000}{36}\right) \hat{y}$
$= - 1.80 \overline{5} \times {10}^{4} \hat{y} {\text{ kgms}}^{-} 1$
$\therefore$ Magnitude of momentum $| \vec{p} | = 1.80 \overline{5} \times {10}^{4} {\text{ kgms}}^{-} 1$
Direction of momentum is $- \hat{y}$ or south direction.

Second car has opposite momentum$= 1.80 \overline{5} \times {10}^{4} \hat{y} {\text{ kgms}}^{-} 1$
Its velocity is$= \frac{1}{m} \vec{p}$
$= \frac{1}{2175} \left(1.80 \overline{5} \times {10}^{4} \hat{y}\right)$
$\implies 8.3 \hat{y} {\text{ ms}}^{-} 1$, rounded to one decimal place.