Consider the collision of a 1500-kg car traveling east at 20.0 m/s (44.7 mph) with a 2000-kg truck traveling north at 25 m/s (55
.9 mph). The cars lock together in such a way as to prevent them from separating or rotating significantly. One second before the collision, the car is located at position (x,y) = (-20,0) m and the truck is located at position (x,y) = (0,-25) m. 1. Calculate the x-coordinate of the center of mass of the two-automobile system, xCM, one second before the collision. ________ m
2. Calculate the y-coordinate of the center of mass of the two-automobile system, xCM, one second before the collision.________ m
3. Calculate the magnitude of the velocity of the center of mass of the two-automobile system, vCM, one second before the collision. ________ m/s
4. Calculate the direction of the velocity of the center of mass of the two-automobile system, vCM one second before the collision. (Give you answer in degrees relative to the positive x-axis which points to the east.)
________ degrees
5. Calculate the magnitude of the velocity of the center of mass of the two-automobile system, vCM, immediately after the collision. ________ m/s
6. Calculate the direction of the velocity of the center of mass of the two-automobile system, vCM immediately after the collision. (Give you answer in degrees relative to the positive x-axis which points to the east.)
________ degrees
The position of the center of mass 1s before the collision is:
where
; ;
; ;
Replacing these values:
where
; ;
; ;
Replacing these values:
The velocity of their center of mass is:
where
; ;
; ;
Replacing these values:
where
; ;
; ;
Replacing these values:
So, the magnitude of the velocity is:
The angle of the velocity is:
Since on any collision, the velocity of the center of mass is preserved, then the velocity after the collision is the same as the previously calculated value of 16.66m/s at 59.0° due north of east