Question

Two cars of the same mass approach an extremely icy four-way perpendicular intersection. Car A travels northward at 30 m/s, and car B is traveling eastward. They collide and stick together, traveling at 28° north of east. What was the initial velocity of car B?

a) 15 m/s eastward
b) 20 m/s eastward
c) 25 m/s eastward
d) 30 m/s eastward

Answer 1

The initial velocity of car B is 0 m/s eastward.

Step-by-step explanation:

The initial velocity of car B can be determined by considering the vectors of its velocity components before and after the collision. Since car A is traveling northward and car B is traveling eastward, the resulting velocity of the two cars after the collision can be found using vector addition. We can use the law of cosines to solve for the magnitude of the resulting velocity:

vresultant = sqrt((vx1 + vx2)^2 + (vy1 + vy2)^2)

Plugging in the given values, we have:

vresultant = sqrt((30*cos(28))^2 + (30*sin(28) + vy2)^2)

We can solve for vy2 by dividing the equation into its x and y components:

vx1 + vx2 = 30*cos(28)

vy1 + vy2 = 30*sin(28)

Since the x-component of car B's velocity is what we're interested in, we can solve for vx2:

vx2 = vresultant*cos(28) - 30*cos(28)

Calculating the value gives us:

vx2 = 30*cos(28) - 30*cos(28)

vx2 = 0 m/s

Therefore, the initial velocity of car B is 0 m/s eastward.