Acar heading north collides at an intersection with a truck of the same mass as the car heading east. if they lock together and travel at 28 m/s at 27° north of east just after the collision, how fast was the car initially traveling? assume that any other unbalanced forces are negligible.
a. 25 m/s
b. 13 m/s
c. 19 m/s
d. 50 m/s

Initial speed of car = 25 m/s north direction

correct option is A. 25 m/s

Explanation:

given data

Final velocity of both = 28 m/s at 27 degrees north of east

to find out

how fast was the car initially traveling

solution

we consider both vehicle have same mass

mass of car  m1  = mass of truck m2

so we will apply here conservation of momentum  law

m1 × u1 j + m2 × u2 i  = (m1 + m2) × ( v cosθ i + v sinθ j )      1

here m is mass and u is initial velocity and v is final velocity

m × u1 j + m × u2 i  = (2m) × ( 28 × cos27 i + 28 × sin27 j )  

u2 i + u1 j = 2 ( 24.94 i + 12.71 j)

u2 i + u1 j = 49.88 i + 25.42 j

so compare both side we get

Initial speed of car u1 = 25.42 m/s north direction

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