Suppose a small compact car with a mass of 1000 kg is traveling north on Morewood Avenue at a speed of 15 m/s. At the intersection of Morewood and Fifth Avenues, it collides with a truck with a mass of 2000 kgthat is traveling east on Fifth Avenue at 10 m/s. It’s now 2 seconds after the collision has occurred. Fortunately, all occupants were wearing seat belts and there were no injuries, but the two vehicles became thoroughly tangled and moved away from the point of impact as one mass. The insurance adjuster has asked you to help find the velocity of the wreckage just after impact.
Suppose that just before the collision, the driver of the car swerves, so that the car is still traveling at a speed of 15 m/s, but in the direction of 13? east of north when the car collides with the truck. If the two vehicles stick together after the collision, find the magnitude of the velocity of the wreckage.
Express your answer in meters per second to two significant figures.
Referring to Part A, find the direction of the velocity of the wreckage.
Express your answer in degrees to two significant figures. The angle should be measured counterclockwise from the +x axis.
m1(car) = 1000 kg
v1 = 15*sin13i + 15*cos13 j
m2(truck) = 2000 kg
v2 = 10 i
initial momentum Pi = m1*v1 + m2*v2
after collision
final momentum Pf = (m1+m2)*v
from momentum conservation
Pf = Pi
(m1 + m2)*V = m1*v1 + m2*v2
(1000 + 2000)*V = (1000*15*sin13i )+ (1000*15*cos13j) + (2000*10
i)
3000*V = 3374.26 i + 14615.55 j + 20000 j
V = 7.79 i + 4.87 j
magnitude = sqrt(7.79^2+4.87^2) = 9.2 m/s
part(B)
direction = tan^-1(4.87/7.79) = 32 degrees east of north
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