A car heading north suddenly collides at an intersection with a truck of the same mass heading east. If they lock together and travel at 28 m/s at $15 ^ { \circ }$ north of east just after the collision, how fast was the car initially traveling?
A) 7 m/s
B) 28 m/s
C) 11 m/s
D) 14 m/s

Question

A car heading north suddenly collides at an intersection with a truck of the same mass heading east. If they lock together and travel at  28 m/s at $15 ^ { \circ }$ north of east just after the collision, how fast was the car initially traveling?
A)  7 m/s
B)  28 m/s
C)  11 m/s
D)  14 m/s

Quizplus · Accepted Answer

Using conservation of momentum, the northward component of the velocity after the collision is equal to the initial velocity of the car. The northward component is $28 \sin(15^\circ)$, which equals approximately 7.24 m/s. Since the car and truck have the same mass, the car's initial velocity is twice this component, approximately 14 m/s.

A Car Heading North Suddenly Collides at an Intersection with a Truck