A 900- kg car collides with a 1200- kg car that was initially at rest at the ori

Question

A 900- kg car collides with a 1200- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 10.0 km/h in a direction of 30 degree with respect to the positive x axis. The heavier car moves at 13 km/h at -50.0 with respect to the positive x axis. What was the initial speed of the lighter car (in km/h)? The car is not coming in along the x-axis in the picture. Calculate the x and y values of the initial momenta and compute the speed and direction of the velocity. What was the initial direction (as measured counterclockwise from the x-axis)?

Explanation / Answer

Applying momentum conservation for the collision,

initial = final momentum of two car system

900 (v cos(theta)i + v sin(theta)j ) = 900 ( 10 cos30i + 10 sin30j) + 1200 (13 cos50i - 13 sin50j )

v cos(theta)i + v sin(theta)j = 8.66i + 5j + 11.14i - 13.28j

v cos(theta) = 19.8 ,...... (i)

v sin(theta) = 8.28 .... (ii)

(ii)/(i) => tan(theta) = 8.28 / 19.8

theta = 22.7 deg

v = 19.8 / cos22.7 = 21.5 km / h ..........Ans

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