Answer:
The direction of the joint velocity after the collision is northeast.
Step-by-step explanation:
To find the direction of the joint velocity after the collision, we can use the following steps:
Calculate the total momentum of the system before the collision.
Total momentum before collision = (3520 kg)(26.0 m/s) + (1480 kg)(13.0 m/s)
= 112,560 kg m/s east
Use conservation of momentum to find the total momentum of the system after the collision.
Total momentum after collision = (3520 kg + 1480 kg) * v
where v is the final velocity of the system.
Set the two momentum expressions equal to each other and solve for v.
(3520 kg)(26.0 m/s) + (1480 kg)(13.0 m/s) = (5000 kg) * v
v = 22.3 m/s
Look at the initial momentum vectors and the final momentum vector to determine the direction of the final velocity.
The initial momentum vectors are pointing north and east, respectively. The final momentum vector must be in between these two vectors, since the total momentum of the system has not changed. Therefore, the direction of the final velocity is northeast.
Conclusion: The direction of the joint velocity after the collision is northeast.