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?

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

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

It seems like you have followed a valid approach by breaking down the velocities into their respective x and y components and then using the Pythagorean theorem to find the magnitude of the combined velocity. However, there might be a mistake in your calculations. Let's go through the correct steps.

To find the magnitude of the combined velocity after the collision, we need to add the x and y components of the velocity for each object. Let's start by finding the x component of the velocity for each object:

Baseball:
Mass (m1) = 145 g = 0.145 kg
Velocity (v1) = 5 m/s * cos(180 degrees) = -5 m/s (negative sign indicates a westward direction)

Ball of clay:
Mass (m2) = 290 g = 0.29 kg
Velocity (v2) = 4 m/s * cos(135 degrees) = -2.8284 m/s (negative sign indicates a westward direction)

Now, let's find the y component of the velocity for each object:

Baseball:
Velocity (v1) = 5 m/s * sin(180 degrees) = 0 m/s

Ball of clay:
Velocity (v2) = 4 m/s * sin(135 degrees) = 2.8284 m/s

Now, we can add the x and y components of velocity for each object:

x-component: -5 m/s + (-2.8284 m/s) = -7.8284 m/s
y-component: 0 m/s + 2.8284 m/s = 2.8284 m/s

Next, we can calculate the magnitude of the combined velocity using the Pythagorean theorem:

magnitude = sqrt((-7.8284 m/s)^2 + (2.8284 m/s)^2) = 8.33 m/s (rounded to two decimal places)

Therefore, the correct magnitude of the combined velocity after they collide and stick together is approximately 8.33 m/s.