A car 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