Question

A loaded transport truck with a mass of $38000kg$ is travelling at $1.2\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$ ,what will be the velocity of a $1400kg$car if it has the same momentum?

Answer 1

Step-1: Given dat

Mass of the truck = ${\mathrm{M}}_{\mathrm{truck}}=38000\mathrm{kg}$

Mass of the car =${\mathrm{M}}_{\mathrm{car}}=1400\mathrm{kg}$

Velocity of truck = ${\mathrm{V}}_{\mathrm{truck}}=1.2\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$

Velocity of car = ${\mathrm{V}}_{\mathrm{car}}=?$

Momentum of car = Momentum of truck

Step-2: Formula used

Momentum= $\mathrm{P}=\mathrm{m}\times \mathrm{v}$

Step-3: Calculation

Momentum of car = Momentum of truck

${\mathrm{P}}_{\mathrm{car}}={\mathrm{P}}_{\mathrm{truck}}$

${\mathrm{M}}_{\mathrm{car}}\times {\mathrm{V}}_{\mathrm{car}}={\mathrm{M}}_{\mathrm{truck}}\times {\mathrm{V}}_{\mathrm{truck}}$

$1400\times {\mathrm{V}}_{\mathrm{car}}=38000\times 1.2$

${\mathrm{V}}_{\mathrm{car}}=\frac{38000\times 1.2}{1400}=\frac{380\times 1.2}{14}=32.58\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Hence, The velocity of car is $32.58\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$.