A 1100- kg car collides with a 1300- kg car that was initially at rest at the or

Question

A 1100- kg car collides with a 1300- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 30.0 km/h in a direction of 40 o with respect to the positive x axis. The heavier car moves at 33 km/h at -48 o with respect to the positive x axis. What was the initial speed of the lighter car (in km/h)? What was the initial direction (as measured counterclockwise from the x-axis)?

A 1100- kg car collides with a 1300- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 30.0 km/h in a direction of 40 o with respect to the positive x axis. The heavier car moves at 33 km/h at -48 o with respect to the positive x axis. What was the initial speed of the lighter car (in km/h)? What was the initial direction (as measured counterclockwise from the x-axis)?

Explanation / Answer

x axis


m1*ux = m1*V1*cos40 + m2*V2*cos48

1100*ux = 1100*30*cos40 + 1300*33*cos48

ux = 49.1 k/h

y axis

m1*uy = m1*V1*sin40 - m2*V2*sin48

1100*uy =((1100*30*sin40) - (1300*33*sin48))

uy = ?9.7 km /h

u = sqrt(ux^2+uy^2) = 50 km/h

angle = tan^-1(uy/ux) = 11.3 degrees

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