A baseball and a ball of clay are approaching each other. The mass of the baseball is 145 g and it is moving due west 5 m/s at 180 degrees. The ball of clay is 290 g and it is moving northwest at 135 degrees at 4 m/s. What is the magnitude of their combined velocity after they collide and stick together?
I first tried to find velocity in the x direction, then velocity in the y direction, and use the Pythagorean theorem to find total magnitude. I got 1.71 m/s. Why is this wrong? What should I be doing instead?
3 answers
Edit: I now got 3.14 m/s as the answer, which is still wrong.
as the title of your question states
... momentum is conserved
before collision
...x-direction
... baseball ... -5 m/s * 145 g
... clay ... -4 m/s * sin(45º) * 290 g
... sum bb and clay for total x-momentum
... y-direction
... bb ... no y-component
... clay ... 4 m/s * cos(45º) * 290 g
after collision
... (total momentum)^2 = (xmom)^2 + (ymom)^2
... mass is ... bb + clay
... velocity magnitude = (total mom) / mass
... velocity angle ... tan(Θ) = ymom / xmom
... momentum is conserved
before collision
...x-direction
... baseball ... -5 m/s * 145 g
... clay ... -4 m/s * sin(45º) * 290 g
... sum bb and clay for total x-momentum
... y-direction
... bb ... no y-component
... clay ... 4 m/s * cos(45º) * 290 g
after collision
... (total momentum)^2 = (xmom)^2 + (ymom)^2
... mass is ... bb + clay
... velocity magnitude = (total mom) / mass
... velocity angle ... tan(Θ) = ymom / xmom
Thank you! @Scott Using this method though, I get 7.06 as an answer...where am I making an error? 7.06 isn't even an answer choice for this problem? My choices are 9, -0.255, 1.75, and 4.02