# Momentum: 1D collisions A car has a mass of 1850kg. A truck was travelling at 65.1km/hr just before impacting the stationary car from directly behind. After the car and truck lock together, they travelled at 26.2km/hr. The mass of the truck is?

Jun 24, 2016

${m}_{t} = 1246.02 \text{ } k g$

#### Explanation:

$\text{Truck has a momentum before impacting}$

${P}_{t} = m \cdot {v}_{t} = {m}_{t} .65 .1$

$\text{Car has not momentum before impacting}$

${P}_{c} = {m}_{c} \cdot {v}_{c} = 1850 \cdot 0 = 0$

$\text{Total momentum before impacting}$

${P}_{b} = {P}_{t} + {P}_{c} = {m}_{t} \cdot 65.1 + 0 = {m}_{t} \cdot 65.1$

$\text{Momentum after impacting:}$

${P}_{a} = \left({m}_{t} + {m}_{c}\right) \cdot 26.2$

${P}_{a} = \left({m}_{t} + 1850\right) \cdot 26.2$

${P}_{b} = {P}_{a}$

${m}_{t} \cdot 65.1 = \left({m}_{t} + 1850\right) \cdot 26.2$

${m}_{t} \cdot 65.1 = {m}_{t} \cdot 26.2 + 1850 \cdot 26.2$

${m}_{t} \cdot 65.1 - {m}_{t} \cdot 26.2 = 1850 \cdot 26.2$

$38.9 \cdot {m}_{t} = 48470$

${m}_{t} = \frac{48470}{38 , 9}$

${m}_{t} = 1246.02 \text{ } k g$