Question

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

Answer 1

final velocity =
`(13)/(5)` i +
`(52)/(5)` j

magnitude = 10.72

direction = 75.96°

Step-by-step 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 =
`(13)/(5)`

so

as that in Y direction

Mb × 13 = 5Ma × Vx

4 × Ma × 13 = 5Ma × Vx

so

Vy =
`(52)/(5)`

so final velocity will be here

final velocity = Vx i + Vy j

final velocity =
`(13)/(5)` i +
`(52)/(5)` j

and

magnitude will be

magnitude =
`\sqrt{((13)/(5))^2 + ((52)/(5))^2}`

magnitude = 10.72

and

direction is

direction =
`tan^(-1) (4)/(1)`

direction = 75.96°