On a parking lot a 1,000 kg car moving at 15.0 miles per hour in the direction 2

Question

On a parking lot a 1,000 kg car moving at 15.0 miles per hour in the direction 20o North of East collides with a 1,500 kg van moving at 10.0 miles per hour in the direction 10o South of West. As a result of the collision, the vehicles attach to each other. During the collision, all forces acting on the vehicles along the road’s surface can be neglected. (Hint: sketch initial vectors placing them so that they start at the origin.)

A. Find the magnitude and the direction of the vehicles’ velocity immediately after the collision.

B. Is the collision elastic? Explain how you can tell.

C. What % of the net initial kinetic energy was lost in the collision? Where did the lost energy go?

Explanation / Answer

A) initial momentum of system = final momentum

m1v1 + m2v2 = Mv

1000*15*(cos20degree i + sin20degree j) - 1500*10*(cos10degree i + sin10degree j) = (1000+1500)V

14095i +5130j - 14772i - 2605j = 2500v

2500v = -677 i + 2525j

v = -0.27i + 1.01j

V= 1.046 miles/hour

direction = arctan(1.01/0.27)

= 75 degree North of west

B) No, it is inelastic as they stick togather

C)initial KE in (Kg.mile/h)^2 = 0.5×1000×15^2 + 0.5×1500×10^2 = 187500

Final KE =0.5×2500×1.046^2 =1367

% lost KE = 100× ((187500-1367)/187500) =99.27%

It gets converted into heat

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