Question

FIGURE Q36.1 shows two balls. What are the speed and direction of each (a) in a reference frame that moves with ball 1 and (b) in a reference frame that moves with ball 2?

Short answer

a. The speed of ball 2 with respect to ball 1 is $-9\mathrm{m}/\mathrm{s}.$

the speed of ball 1 with itself is zero.

b. The speed of ball 2 with respect to ball 2 is $0\mathrm{m}/\mathrm{s}.$

the speed of ball 1 with respect to ball 2 is$9\mathrm{m}/\mathrm{s}.$

Step-by-step solution

Part (a) Step 1: Given information

We have given, two balls of speed

$$\begin{gathered} \mathrm{Speed}\mathrm{of}\mathrm{ball}1=6\mathrm{m}/\mathrm{s} \\ \mathrm{Speed}\mathrm{of}\mathrm{ball}2=3\mathrm{m}/\mathrm{s}. \end{gathered}$$

We have to find the speed of the each ball with respect to ball 1.

Simplify

Velocity of ball 1 with respect to itself will be always zero. Since for itself reframe it will be in rest.

${\mathrm{u}}_{11}=0$

Velocity of ball 2 with respect to ball 1 is

$$\begin{gathered} {\mathrm{u}}_{21}={\mathrm{u}}_2-\mathrm{V} \\ {\mathrm{u}}_{21}=-3(\mathrm{reverse}\mathrm{direction})-6 \\ {\mathrm{u}}_{21}=-9\mathrm{m}/\mathrm{s} \end{gathered}$$

Part (b) Step 1: Given information

We have given,

$$\begin{gathered} \mathrm{Speed}\mathrm{of}\mathrm{ball}1=6\mathrm{m}/\mathrm{s} \\ \mathrm{Speed}\mathrm{of}\mathrm{ball}2=3\mathrm{m}/\mathrm{s}. \end{gathered}$$

We have to find the speed of each ball with respect to ball 2.

Simplify

Velocity of ball 2 with respect to itself will be always zero. Since for itself reframe it will be in rest.

${\mathrm{u}}_{22}=0$

Velocity of ball 1 with respect to ball 2 is

$$\begin{gathered} {\mathrm{u}}_{12}={\mathrm{u}}_1-\mathrm{v} \\ {\mathrm{u}}_{12}=6-(-3) \\ {\mathrm{u}}_{12}=9\mathrm{m}/\mathrm{s} \end{gathered}$$