125-kg car traveling initially with a speed of 25.0 m/s in an easterly direction crashes into the rear end of a 8,700-kg truck moving in the same direction at 20.0 m/s. The velocity of the car right after the collision is 18.0 m/s to the east. What is the velocity of the truck right after the collision
Answer:
The velocity of truck after collision is 20.1 [tex]\frac{m}{s}[/tex]
Explanation:
Given:
Mass of car [tex]m_{c} = 125[/tex] kg
Initial velocity of car [tex]v_{i} = 25 \frac{m}{s}[/tex]
Mass of truck [tex]m_{t} = 8700[/tex] kg
Initial velocity of truck [tex]v_{t} = 20\frac{m}{s}[/tex]
Velocity of car after the collision [tex]v_{c} = 18 \frac{m}{s}[/tex]
For finding the velocity of truck after the collision,
According to the linear momentum conservation
[tex]m_{c} v_{i} + m_{t} v_{t} = m_{c} v_{c} + m_{t} v'[/tex]
Where [tex]v’ =[/tex] velocity of truck after the collision,
[tex]125 \times 25 + 8700 \times 20 = 125 \times 18 + 8700 v'[/tex]
[tex]v’ = 20.1\frac{m}{s}[/tex]
Therefore, the velocity of truck after collision is 20.1 [tex]\frac{m}{s}[/tex]