The figures below show bird\'s-eye views of six automobile crashes an instant be

Question

The figures below show bird's-eye views of six automobile crashes an instant before they occur. The automobiles have different masses and incoming velocities as shown. After impact, the automobiles remain joined together and skid to rest in the direction shown by vfinal . Rank these crashes according to the angle ?, measured counterclockwise as shown, at which the wreckage initially skids.

Rank from largest to smallest. To rank items as equivalent, overlap them.

Vfinal 15 m/s e Vfinal Vfinal Vfinal 9 m/s Vfinal 7 m/s Vfinal 7 m/s 10 m/s 1000 kg 10 m/s 1200 kg 1000 kg 10 m/s 700 kg 15 m/s 1000 kg 10 m/s 1000 kg 7 m/s 7 m/s 700 kg 1500 kg 10 m/s 1000 kg 700 kg 1000 kg 1000 kg smallest largest reset ? help The correct ranking cannot be determined

Explanation / Answer

here,

for figure 1 ,

theta 1 = arctan(momentum in y- direction / momentum in x-direction)

theta 1 = arctan(1000*10 /1000 *10)

theta 1 = arctan(1)

theta 1 = 45 degree

for figure 2 ,

theta 2 = arctan(momentum in y- direction / momentum in x-direction)

theta 2 = arctan(1000*7 /1000 *10)

theta 2 = 40 degree

for figure 3 ,

theta 3 = arctan(momentum in y- direction / momentum in x-direction)

theta 3 = arctan(700*7 /700 *7)

theta 3 = 45 degree

for figure 4,

theta 4 = arctan(momentum in y- direction / momentum in x-direction)

theta 4 = arctan(1000*10 /1000 *7)

theta 4 = 55 degree

for figure 5 ,

theta 5 = arctan(momentum in y- direction / momentum in x-direction)

theta 5 = arctan(700*15 /1200 * 9)

theta 5 = 44.2 degree

for figure 6 ,

theta 6 = arctan(momentum in y- direction / momentum in x-direction)

theta 6 = arctan(1500*10 /1000 *15)

theta 6 = 45 degree   

on compairing all the values of theta

theta 4 > (theta 1 = theta 3 = theta 6) > theta 5 > theta 2

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