Question

2D Car Collision

Car Collision in 2D (c7p50) A 900- kg car collides with a 1400- 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 35 degrees with respect to the positive x axis. The heavier car moves at 13 km/h at -41 degrees with respect to the positive x axis.

A) What was the initial speed of the lighter car (in km/h)? ____Tries 0/7

B) What was the initial direction (as measured counterclockwise from the x-axis)? ___Tries 0/7

Answer 1

We know that after the collision, Momentum will remain conserved, So

Using Momentum conservation in x-direction:

Pix = Pfx

m1*u1x + m2*u2x = m1*v1x + m2*v2x

m1 = mass of lighter car = 900 kg

m2 = mass of blue heavier car = 1400 kg

u1x = Initial velocity of m1 in x-direction = ? m/sec

u2x = Initial velocity of m2 in x-direction = 0 m/sec

After the collision lighter car moves at 10.0 km/hr at 35 deg w.r.t. +ve x-axis

v1 = 10 km/hr = 10*5/18 = 2.78 m/sec

v1x = Final velocity of m1 in x-direction = 2.78*cos 35 deg = 2.28 m/sec

After the collision heavier car moves at 13 km/hr at -41 deg w.r.t. +ve x-axis

v2 = 13 km/hr = 13*5/18 = 3.61 m/sec

v2x = Final velocity of m2 in x-direction = 3.61*cos 41 deg = 2.72 m/sec

So,

900*u1x + 1400*0 = 900*2.28 + 1400*2.72

u1x = (900*2.28 + 1400*2.72)/900

u1x = 6.51 m/sec

Now Using Momentum conservation in y-direction:

Piy = Pfy

m1*u1y + m2*u2y = m1*v1y + m2*v2y

u1y = Initial velocity of m1 in y-direction = ? m/sec

u2y = Initial velocity of m2 in y-direction = 0 m/sec

v1y = Final velocity of m1 in y-direction = 2.78*sin 35 deg = 1.59 m/sec

v2y = Final velocity of m2 in y-direction = -3.61*sin 41 deg = -2.37 m/sec

So,

900*u1y + 1400*0 = 900*1.59 + 1400*(-2.37)

u1y = (900*1.59 + 1400*(-2.37))/900

u1y = -2.10 m/sec

Now Initial velocity of lighter car will be:

u1 = u1x i + u1y j

u1 = 6.51 i - 2.10 j

Speed of lighter car initially will be:

|u1| = sqrt (6.51^2 + (-2.10)^2)

|u1| = 6.84 m/sec = 6.84*18/5 = 24.6 km/hr

Part B.

Direction = arctan (u1y/u1x) = arctan (-2.10/6.51)

Direction = -17.9 deg w.r.t. the +ve x-axis = 360 - 17.9

Direction = 342.1 deg measured CCW from +ve x-axis

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