Chapter 9, Problem 74A

a.

To determine

To Sketch: The situation of skaters when they hold each other & loose contact with the help of sketch.

Explanation of Solution

Given:

The mass of Diego, $m_D=90\mathrm{kg}$

The mass of Keshia, $m_K=60\mathrm{kg}$

The sketch of the situation is given below :

  

The before and after parameter:

  $\begin{array}{l}\text{Before:}\\ m_D=90\mathrm{kg}\\ m_K=60\mathrm{kg}\\ V_{D_i}=0\text{m/s}\\ V_{K_i}=0\text{m/s}\\ \text{After:}\\ m_D=90\text{kg}\\ m_K=60\text{kg}\\ V_{D_f}=?\text{m/s}\\ V_{K_f}=?\text{m/s}\end{array}$

Conclusion:

The initial velocity of each skater is zero & the mass will be same before & after the event .

b.

To determine

The ratio of velocities just after the hand loose contact.

Answer to Problem 74A

The ratio of velocities just after the hand loose contact is $-1.5$ , here negative sign denotes the opposite direction.

Explanation of Solution

Given:

The mass of Diego, $m_D=90\mathrm{kg}$

The mass of Keshia, $m_K=60\mathrm{kg}$

  $\begin{array}{l}{V}_{D_i}=0\text{m/s}\\ V_{K_i}=0\text{m/s}\end{array}$

Formula Used:

The linear momentum is conserved .

  $\begin{array}{l}{p}_{D_i}+p_{K_i}=0=p_{D_f+}{p}_{K_f}\\ p=mv\\ m_D{V}_{D_i}+m_K{V}_{D_f}=0\\ m_D{V}_{D_f}+m_K{V}_{K_f}=0\\ \frac{V_{K_f}}{V_{D_f}}=-\frac{m_D}{m_K}\end{array}$

Calculation:

As per the given problem

  $\begin{array}{l}{m}_D=90\text{kg}\\ m_K=60\text{kg}\end{array}$

Substitute these values in the formula $\frac{V_{K_f}}{V_{D_f}}=-\frac{m_D}{m_K}$

  $\frac{V_{K_f}}{V_{D_f}}=-\frac{m_D}{m_K}=-\frac{90}{60}=-1.5$

The negative sign shows that the direction of velocities is different .

Conclusion:

The ratio of velocities just after the hand loose contact is -1.5 here negative sign denotes the opposite direction.

c.

To determine

The speed of which skater is greater.

Explanation of Solution

As the weight of Diego is greater than the Keshia so, Keshia has greater speed due to less weight.

Conclusion:

The Keshia has greater speed.

d.

To determine

The skater who pushed harder.

Explanation of Solution

Both skaters pushed each other with equal & opposite forces as per Newtons third law.

Conclusion:

Both will experience same force (pushed ).