please show work for how to get correct answers! Show your caleulations clearly

Question

please show work for how to get correct answers!

Show your caleulations clearly and completely in this section for partial credit! 1. Two cars collided at an intersection. Car A with a mass of 1200 kg is going from east to west with a speed of 15.0 m/s, while car B of mass 1500 kg is going north to south with a speed of 10.0 m/s. As a result of the collision the two cars enmeshed and move with a common speed. (a) Sketch and label the diagram of e collision (b) Calculate their common speed after collision. (C) Calculate the direction after collision (state the direction in terms of north, south, east and west). (d) Prove, by calculation, that the collision is inelastic. 200k 4

Explanation / Answer

1. given

Ma = 1200 kg

Ua = -15 m/s i ( i is unit vectro from west to east and j is unit vectro from south to north)

Mb = 1500 kg

Ub = -10 m/s j

a. the diagram is as shown oin pencil in the figure

b.

now let the final velcity of the smushed cars after the collisiosn be V

then from conservation of momentum

MaUa + MbUb = (Ma + Mb)V

-18,000i - 15,000j = 2700*V

V = -6.6667i - 5.5556j m/s

so speed, |V| = sqroot(Vx^2 + Vy^2) = 8.67 m/s

c. direction of motion makes angle theta south of west

then

tan(theta) = 5.55556/6.6667

theta = 39.805 deg

d. initial KE of the system = 0.5Ma*Ua^2 + 0.5*Mb*Ub^2 = 210000 J

final KE of the system = 0.5(Ma + Mb)|V|^2 = 101478.015 J

hence as final KE !+ initial KE hence the collision is inelastic

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