Question

A girl, moving at 8 m/s on in-line skates, is overtaking a boy moving at 5m/s as they both skate on a straight path. The boy tosses a ball backward toward the girl, giving it speed 12 m/s relative to him. What is the speed of the ball relative to the girl, who catches it?

(a) $\mathbf{\text{(8 + 5 + 12)}}\mathbf{}\mathbf{\text{m/s}}$

(b) $\mathbf{\text{(8 - 5 - 12)}}\mathbf{}\mathbf{\text{m/s}}$

(c) $\mathbf{\text{(8 + 5 - 12)}}\mathbf{}\mathbf{\text{m/s}}$

(d) $\mathbf{\text{(8 - 5 + 12)}}\mathbf{}\mathbf{\text{m/s}}$

(e) $\mathbf{\text{( - 8 + 5 + 12)}}\mathbf{}\mathbf{\text{m/s}}$

Short answer

A car moving around a circular track with constant speed have an acceleration directed toward the centre of its path

So, option d is correct

Step-by-step solution

Step 1: Define velocity

The change in displacement that has occurred in the unit time interval is called velocity. Velocity is generally calculated in a particular direction. It is a vector quantity.

Explanation for correct option

Girl's speed in relation to the ground,

${\mathrm{v}}_{\text{girl, ground}}=8\mathrm{m}/\mathrm{s}$

Boy's speed in relation to the ground,

${\mathrm{v}}_{\text{boy, ground}}=5\mathrm{m}/\mathrm{s}$

Consider the boy's path to be positive.

Velocity of ball relative to boy,

${\mathrm{v}}_{\text{ball,boy}}=\text{-12m/s}$

Velocity of ball

$\begin{array}{rcl}{\mathrm{v}}_{\text{ball,ground}}& =& {\mathrm{v}}_{\text{ball,boy}}+{\mathrm{v}}_{\text{boy,ground}}\\ & =& -12+5\\ & =& -7\mathrm{m}/\mathrm{s}\end{array}$

Velocity of ball relative to girl,

$\begin{array}{rcl}{\mathrm{v}}_{\mathrm{ball},\mathrm{girl}}& =& {\mathrm{v}}_{\mathrm{ball},\mathrm{greund}}+{\mathrm{v}}_{\mathrm{girl},\mathrm{ground}}\\ & =& -7-8\\ & =& -15\mathrm{m}/\mathrm{s}\end{array}$

So is correct option.