A truck of massmT= 2000 kg is going northon Guadalupe with a speed of 4 m/s.Thetruck is struck by an eastbound car (mass of1000 kg) traveling on 24th street.From theskidmarks after the collision, it is deducedthat the mangled wreckage, which sticks to-gether after the collision was skidding at angle20◦with respect to the initial direction of thecar.What was the initial speed of the car?1.14 m/s2.17 m/s3.10 m/s4.5 m/s5.3 m/s6.22 m/s

Assuming no external forces present during the collision, total momentum must be conserved. As momentum is a vector, if we decompose it in two components mutually perpendicular, both components must be conserved too.

We must have into account that after the collision, both masses keep moving together, in a direction 20º North of East.

In our case, it is advisable to project the momentum vector along directions N-S (our y-axis) and W-E (our x-axis), so we can write the following algebraic equations:

Δpx = 0⇒ px₀ = pxf

⇒ mcar*vcar₀ = (mc+mT)* vf* cos 20º

⇒ 1000 kg*vcar₀ = 3000 kg*vf*cos 20º (1)

Δpy = 0 ⇒ py₀ = pyf

⇒ mT*vT₀ = (mc+mT)*vf*sin 20º (2)

⇒2000 kg*4m/s = 3000 kg*vf* sin 20º

Dividing both sides of (2) by (1), we have:

tg 20º = 8000 kg*m/s / 1000 kg*vcar₀

Solving for vcar₀, we get:

vcar₀ = 8 / tg 20º m/s = 22 m/s