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

AI Thread Summary
The discussion centers on calculating the velocity of two colliding carts, C and B, which stick together post-collision. The user initially calculated the momentum of each cart using the equation P=mv and applied the Pythagorean theorem to find the resultant momentum of the combined cart. However, the calculated velocity of 8.5 m/s was disputed, with the correct answer being 7.8 m/s. The discrepancy arises from a miscalculation in the momentum values or the application of the conservation of momentum principle. The conversation highlights the importance of accurately applying physics equations in collision scenarios.
jacegalvin
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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?
 
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the answer must be 8.5 m/s, i got the same by using vectors.
 
8.5 seems correct
 

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