What Went Wrong in Calculating the Velocity of Carts C and B After Collision?

[jacegalvin]

Homework Statement

:
A cart 'C' mass of 2 tonnes is launched at 10m/s towards Cart 'B' which is 3 tonnes and moving at 12.5m/s. The angle between their paths of motion is 90 degrees. When the 2 carts collide, they remain stuck together. what is the velocity of the stuck together cart 'CB'
assuming no friction.

Homework Equations

P=mv
Pfinal=Pinitial
c= √b²+c²

The Attempt at a Solution

what i assumed was you could create a right angle triangle, with momentum of Cart C as one side, momentum of Cart B as another and the hypotenuse would be momentum of cart CB

So therefore:
Pbc= √Pb²+Pc²
Pbc=√(3000x12.5)²+(2000x10)²
Pbc=√1406250000+400000000
Pbc=4250
Pbc=m(c+b)v
4250=5000v
v=8.5m/s

but apparently the answer is 7.8m/s
what have i done wrong?

 

[supratim1]

the answer must be 8.5 m/s, i got the same by using vectors.

 

[ashishsinghal]

8.5 seems correct