You are investigating a car wreck. Mr. Q was traveling east in a 816.5 kg car and collided with Ms. X who was traveling south in a 997.9 kg car. The cars stuck together and the skid marks indicate that they moved in a direction of 325 degrees after the collision. Both drivers claim to have been driving the speed limit of 20.1 m/s. Show mathematically that one of them has to be lying.
I know this has to do with conservation of momentum and tangent, but I don't have any idea how to solve it. Somehow I'm supposed to show that the angle would have to equal 309 degrees instead of 325.
I know this has to do with conservation of momentum and tangent, but I don't have any idea how to solve it. Somehow I'm supposed to show that the angle would have to equal 309 degrees instead of 325.
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Problem is, if one is travelling east and one is travelling south, they would not end up travelling 325 degrees, which is west of north. Do I assume the direction is FROM 325 degrees? Or their directions were FROM east and south? Better stick with the latter.
Angles. Atan (816.5/ 997.9) = 39.28 degrees.
(90 - 39.28) = 50.72 degrees.
The more massive car, if both were travelling the speed limit, is going to knock the less massive one off course further, = the 50.72 degrees.
(360 - 50.72) = 309.28 degrees.
Thus, assuming one was being truthful and really had been travelling at the speed limit, and as the angle was greater than 309.28, Ms. X was speeding.
Angles. Atan (816.5/ 997.9) = 39.28 degrees.
(90 - 39.28) = 50.72 degrees.
The more massive car, if both were travelling the speed limit, is going to knock the less massive one off course further, = the 50.72 degrees.
(360 - 50.72) = 309.28 degrees.
Thus, assuming one was being truthful and really had been travelling at the speed limit, and as the angle was greater than 309.28, Ms. X was speeding.