Show all your work to get full credit including the equation(s) used without num

Question

Show all your work to get full credit including the equation(s) used without numbers in them, and plug in numbers into the equation. Answers must have proper units and significant figures. Only equations on the equations list can be used. Any other equations must be derived from the ones on the list. Only 4 problems will be graded. If you do all 5 problems, I will only grade the first 4. It is not the best 4 out of 5. Each problem must have a pictorial and mathematical representation. A car (m_1 = 1950 kg) is moving 12.3 degree north of west on a road at 26.9 m/s. Another car (m_2 = 1230 kg) is moving 38.2 degree east of north on another road at 39.2 m/s. A third car (m_3 = 1550 kg) is moving along a third road. The three cars collide, stick together, and move with a velocity of 15.3 m/s due north. Find the magnitude and direction (from the east) of the velocity of the third car before collision.

Explanation / Answer

Applying momentum conservation,

[1950 x 26.9 x (-cos12.3i + sin12.3j) ] + [ 1230 x 39.2 (sin38.2i + cos38.2j)] + [ 1500 v3] = (1950 + 1230 + 1500) (15.3j)

[ -51250.9 i + 11174.5 j] + [ 29817.2i + 37890.8j] + [ 1500 v3] = 71604j

1500v3 = 21433.9i + 22538.7j

v3 = 14.3i + 15.03j

magnitude = sqrt(14.3^2 + 15.03^2) = 20.74 m/s

Direction = tan^-1(15.03 / 14.3) = 46.4 deg

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