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Two vehicles approach a right angle intersection and then suddenly collide. After the collision, they become entangled. If their mass ratios were 1:4 and their respective speeds as they approached the intersection were both 13 m/s, find the magnitude and direction of the final velocity of the wreck. Group of answer choices

Respuesta :

Answer:

final velocity = [tex]\frac{13}{5}[/tex] i +  [tex]\frac{52}{5}[/tex] j

magnitude = 10.72

direction = 75.96°

Explanation:

solution

we will consider here  

Va = 13 i

 and

Vb = 13 j

so both are entangled after collision,

it will be

Ma × Va + Mb × Vb = (Ma+Mb) × V    ........................1

here

Mb = 4 Ma

so that in the x direction will be

Ma × 13 = 5 Ma × Vx

so

Vx = [tex]\frac{13}{5}[/tex]

so

as that in Y direction  

Mb × 13 = 5Ma × Vx

4 × Ma × 13 = 5Ma × Vx

so

Vy = [tex]\frac{52}{5}[/tex]

so  final velocity will be here

final velocity = Vx i + Vy j

final velocity = [tex]\frac{13}{5}[/tex] i +  [tex]\frac{52}{5}[/tex] j

and

magnitude will be

magnitude = [tex]\sqrt{(\frac{13}{5})^2 + (\frac{52}{5})^2}[/tex]

magnitude = 10.72

and

direction is

direction = [tex]tan^{-1} \frac{4}{1}[/tex]

direction = 75.96°

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