In this problem we will consider the collision of two cars initially moving at r

Question

In this problem we will consider the collision of two cars initially moving at right angles. We assume that after the collision the cars stick together and travel off as a single unit. The collision is therefore completely inelastic. The two cars shown in the figure, of masses and , collide at an intersection. Before the collision, car 1 was traveling eastward at a speed of , and car 2 was traveling northward at a speed of . (Figure 1) After the collision, the two cars stick together and travel off in the direction shown.

Explanation / Answer

when the collison in perpendicular or in 2 dimension then Vcm,x=((m1*v1,x)+(m2*v2,x))/(m1+m2) where cm is centre of mass and v2,x=0 because there is no velocity of car 2 in x direction Vcm,x= m1*v1,x/(m1+m2) similarly for Vcm,y= m2*v2,y/(m1+m2) it is the component of the velocity of the centre of mass, so the magnitude is: Vcm= sqrt(vcm,x^2 +Vcm,y^2) the tangent of the angle is theta =tan inverse (Vcm,y/Vcm,x) c) when theta is equal to 1 then magnitude of the moment of the cars should be equal Vcm,x=Vcm,y this implies m1*V1,x=m2* V2,y

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