Answer:
[tex]V=4.7km/h[/tex]
[tex]theta=61.9[/tex]°
θ is the angle that goes from the positive x axis to the positive y axis
Explanation:
The skaters collide in a completely inelastic collision, in other words they have the same velocity after the collision, this velocity has a magnitude V and an angle respect the axis X.
We need to use the conservation of momentum Law, the total momentum is the same before and after the collision.
In the axis X:
[tex]m_{1}*v_{ox}=(m_{1}+m_{2})Vcos\theta[/tex] (1)
In the axis Y:
[tex]m_{2}*v_{oy}=(m_{1}+m_{2})Vsin\theta[/tex] (2)
We solve the last equations, we divide them:
[tex]tan\theta=\frac{m_{2}*v_{oy}}{m_{1}*v_{ox}}[/tex]
[tex]theta=arctan{\frac{m_{2}*v_{oy}}{m_{1}*v_{ox}}}[/tex]
[tex]theta=arctan{\frac{75*7.5}{60*5}}=61.9[/tex]°
θ is the angle that goes from the positive x axis to the positive y axis
We add the squares of the equations (1) and (2):
[tex]m_{1}^{2}*v_{ox}^{2}+m_{2}^{2}*v_{oy}^{2}=(m_{1}+m_{2})^{2}V^{2}[/tex]
[tex]V=\frac{\sqrt{m_{1}^{2}*v_{ox}^{2}+m_{2}^{2}*v_{oy}^{2}}}{(m_{1}+m_{2})}[/tex]
[tex]V=4.7km/h[/tex]
