a truck moving +11.0 m/s makes a head - on inelastic collision with a stationary 1290 kg car. after, they…

Explanation:

Step1: Apply the law of conservation of momentum

The law of conservation of momentum states that (p_{initial}=p_{final}). The initial momentum is the momentum of the truck ((m_{truck}v_{truck})) since the car is stationary ((v_{car} = 0), so (p_{car - initial}=0)). The final momentum is ((m_{truck}+m_{car})v_{final}). So the equation is (m_{truck}v_{truck}=(m_{truck}+m_{car})v_{final}). Let (m_{truck}=m), (v_{truck}=11.0\ m/s), (m_{car} = 1290\ kg), (v_{final}=8.75\ m/s). Then (m\times11=(m + 1290)\times8.75).

Step2: Expand and solve for (m)

Expand the right - hand side: (11m=8.75m+1290\times8.75). Subtract (8.75m) from both sides: (11m-8.75m=1290\times8.75). (2.25m = 1290\times8.75). Then (m=\frac{1290\times8.75}{2.25}). Calculate (1290\times8.75 = 11193.75). (m=\frac{11193.75}{2.25}=4975).

Answer:

4975