A 1000- kg car collides with a 1500- kg car that was initially at rest at the or

Question

A 1000- kg car collides with a 1500- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 25.0 km/h in a direction of 35 o with respect to the positive x axis. The heavier car moves at 28 km/h at -50 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)?

The car is not coming in along the x-axis in the picture. Calulate the x and y values of the initial monenta and compute the speed and direction of the velocity.

Explanation / Answer

Resolving into components after collision

X comp of momentum of 1500 kg is final Pf along x = mVx cos theta

P1xf = 1500 * 28 * cos (-50) = 26997.07 kg km/hr

X comp of 1000 kg car   

P2xf = 1000* 25 * cos 35 = 20478.8 K km/hr

total x comp = 26997.07 + 20478.8 = 47475.87 Kg km/hr

Y comp of 1500 kg is P1yf = 1500 * 28 * sin (-50) = -32173.866 Kgkm/hr

Y comp of 1000 kg is P2yf = 1000 * 25 * sin 35 = 14339.41 Kg km/hr

total Y compt = -32173.866 + 14339.41 = -17834.456 kg km/hr

magnitude of momentum P^2 = Px^2 = Py^2

P^2 = 47475.87 ^2 + (-17834.45)^2

P = 50715.14 kg km/hr

Intial speed = 50715.14/-00

Vx = 50.75 kmph

------------------------------

tan theta = Py/Px

tan theta = -17834.456/47475.87

theta = -20.58 deg

or as measured from counter clock wise from x axis

= 360- 20.58   

= 339.41 deg

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