We are given that a sphere Z moves with a relative speed of 1 m/s with respect to sphere X which moves at 5 m/s. Let's draw the velocity vectors of the spheres:
Where:
[tex]\begin{gathered} v_x=\text{ velocity of sphere x} \\ v_z=\text{ velocity of sphere z} \end{gathered}[/tex]
From the relative velocity equation we have:
[tex]v_z=v_r+v_x[/tex]
Where:
[tex]v_r=\text{ velocity of z relative to x}[/tex]
Since we are given the relative velocity we can plug in the values to get the velocity of "z":
[tex]\begin{gathered} v_z=1\frac{m}{s}+5\frac{m}{s} \\ \\ v_z=6\frac{m}{s}_{} \end{gathered}[/tex]
Now, we do the same but now using the sphere Y:
Now, we use the relative velocity equation for these velocities:
[tex]v_z=v_r+v_y[/tex]
In this case, we have that:
[tex]v_r=\text{ velocity of z with respect to y}[/tex]
Now, we subtract the velocity of "y" from both sides:
[tex]v_z-v_y=v_r[/tex]
Substituting the values:
[tex]6\frac{m}{s}-2\frac{m}{s}=v_r[/tex]
Solving the operations:
[tex]4\frac{m}{s}=v_r[/tex]
Therefore, the velocity of "Z" relative to "Y" is 4 m/s.
