Respuesta :
Answer:
The final velocity of the cars is 8.38 m/s at an angle 39.1° south of west.
Explanation:
Given that,
Mass of first car = 1100 kg
Velocity of first car = 8.5 m/s
Mass of second car = 650 kg
Velocity of second car = 17.5 m/s
Suppose we need to find the final velocity of the cars and direction of the cars.
We need to calculate the velocity of the car in west direction
Using conservation of momentum in west direction
[tex]m_{f}v_{f}+m_{s}v_{s}= (m_{f}+m_{s})v_{x}[/tex]
[tex]v_{x}=\dfrac{m_{f}v_{f}+m_{s}v_{s}}{(m_{f}+m_{s})}[/tex]
Put the value into the formula
[tex]v_{x}=\dfrac{1100\times0+650\times17.5}{1100+650}[/tex]
[tex]v_{x}=6.5\ m/s[/tex]
We need to calculate the velocity of the car in south direction
Using conservation of momentum in south direction
[tex]m_{f}v_{f}+m_{s}v_{s}= (m_{f}+m_{s})v_{y}[/tex]
[tex]v_{y}=\dfrac{m_{f}v_{f}+m_{s}v_{s}}{(m_{f}+m_{s})}[/tex]
Put the value into the formula
[tex]v_{y}=\dfrac{1100\times8.5+650\times0}{1100+650}[/tex]
[tex]v_{y}=5.3\ m/s[/tex]
We need to calculate the final velocity of the cars
Using formula of velocity
[tex]v_{eq}=\sqrt{(6.5)^2+(5.3)^2}[/tex]
[tex]v_{eq}=8.38\ m/s[/tex]
We need to calculate the direction
Using formula of direction
[tex]\tan\theta=\dfrac{v_{y}}{v_{x}}[/tex]
Put the value into the formula
[tex]\tan\theta=\dfrac{5.3}{6.5}[/tex]
[tex]\theta=\tan^{-1}(\dfrac{5.3}{6.5})[/tex]
[tex]\theta=39.1^{\circ}[/tex]
Hence, The final velocity of the cars is 8.38 m/s at an angle 39.1° south of west.
