By plugging in the values for v and θ, we get a value of 14.25 m/s for vx. A similar procedure is used to find the y-component of the velocity vector, which is given by: v ⃗_y=v ⃗ sinθ (4)
Where vy represents the y component of the velocity vector in m/s, v is the velocity vector’s magnitude in m/s, and θ is the angle formed between the velocity vector v and the x-axis. Again, we plug in the appropriate values for v and θ, and we get a value of 8.23 m/s for vy. Armed with these values, we can move onto the last phase of this problem: application of the principle of conservation of momentum for inelastic collisions. In collisions where momentum is conserved, all individual component momenta are conserved independently. That is, the y-momentum conservation is not dependent on the x-momenta and vice versa. To make the math for this problem easier, we shall say that the north-south axis will be our y-axis and the east-west axis is our x-axis. For inelastic collisions – ones in which two bodies collide to become one with a common mass and velocity – the x and y momentum conservations are given by: m_1 v ⃗_x1i+m_2 v ⃗_x2i=(m_1+m_2)v ⃗_xf (5) m_1 v ⃗_y1i+m_2 v ⃗_y2i=(m_1+m_2)v ⃗_yf