Please show every step. Thanks in advance! Problem 12. Two cars (let mA = mB = 1

Question

Please show every step. Thanks in advance!

Problem 12. Two cars (let mA = mB = 1000 kg) collide and get so mangled they stick together and slide off as one object. Use uA = 13 m/s and Theta = 55 Degree. The speed limit was 15.6 m/s (equivalent to 35 mph). The driver of car B says he was not speeding. Determine vB and see if he was telling the truth. Problem 13. Two curling stones one red and one yellow are involved in an elastic glancing collision. The yellow stone is initially at rest and is struck by the red stone moving with a speed ilia After the collision the red stone moves along a direction that makes an angle Theta with its initial direction of motion. The velocities of the two stones are perpendicular after the collision. Determine the final speed of each stone.

Explanation / Answer

12)Conserving horizontal momentum,

mava=(ma+mb)vfcos(theta)

1000*13=2000*vfCos55

Conserving vertical momentum,

1000*vb=2000*vfSin55

Solving for vb and vf

vb=18.57m/s

vf=11.33m/s

Clearly he was speeding.

13)Conserving momentum in the direction of the red stone,

mvi=mv1Cos(theta)+mv2Cos(90-theta)

vi=v1Cos(theta)+v2Sin(theta)

Conserving vertical momentum,

0=mv1Sin(theta)-mv2Sin(90-theta)

v1Sin(theta)=v2Cos(theta)

v2=v1 Tan(theta)

Substituting in first equation,

vi=v1Cos(theta)+v1Tan(theta)Sin(theta)

v1=vi/(Cos(theta)+Sin^2(theta)/Cos(theta))=viCos(theta)/(Cos^2(theta)+Sin^2(theta))=viCos(theta)

v2=v1Tan(theta)=viSin (theta)

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