Problem 8.29: Accident Analysis. Two cars collide at an intersection. Car A , wi
ID: 1260754 • Letter: P
Question
Problem 8.29: Accident Analysis.
Two cars collide at an intersection. Car A, with a mass of 1900kg , is going from west to east, while car B, of mass 1500kg , is going from north to south at 15.0m/s . As a result of this collision, the two cars become enmeshed and move as one afterwards. In your role as an expert witness, you inspect the scene and determine that, after the collision, the enmeshed cars moved at an angle of 65.0? south of east from the point of impact.
Part A
How fast were the enmeshed cars moving just after the collision?
Part B
How fast was car A going just before the collision?
Explanation / Answer
Add the momentum vectors.
A has a momentum Pa = 1900 * Va angle 0
B has a momentum Pb = 1500 * 15 angle (-90) = 22500 angle (-90)
R has momentum R = R angle (-65)
Ax = 1900 * Va
Bx = 0
Rx = Rcos(-65)
Ay = 0
By = -22500
Ry = Rsin(-65)
summing x and y
1900 * Va = Rcos(-65)
-22500 = Rsin(-65)
which gives
R = 24826
1900 * Va = Rcos(-65)
1900 * Va = 24826 cos(-65)
Va = 5.52 m/s..........Answer for (b)
total mass is 3400 kg, so if total momentum (R) is 24826, then
Vr = 24826/3400 = 7.3 m/s...........answer for (a)