Question

Relative to sphere at the speed of sphere Z is _ m/s

Answer 1

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:

`\begin{gathered} v_x=\text{ velocity of sphere x} \\ v_z=\text{ velocity of sphere z} \end{gathered}`

From the relative velocity equation we have:

`v_z=v_r+v_x`

Where:

`v_r=\text{ velocity of z relative to x}`

Since we are given the relative velocity we can plug in the values to get the velocity of "z":

`\begin{gathered} v_z=1(m)/(s)+5(m)/(s) \\ \\ v_z=6(m)/(s)_{} \end{gathered}`

Now, we do the same but now using the sphere Y:

Now, we use the relative velocity equation for these velocities:

`v_z=v_r+v_y`

In this case, we have that:

`v_r=\text{ velocity of z with respect to y}`

Now, we subtract the velocity of "y" from both sides:

`v_z-v_y=v_r`

Substituting the values:

`6(m)/(s)-2(m)/(s)=v_r`

Solving the operations:

`4(m)/(s)=v_r`

Therefore, the velocity of "Z" relative to "Y" is 4 m/s.