Chapter 5, Problem 12A

a. Neglecting air resistance, if you throw a baseball at 20 m/s to your friend who is on first base, will the catching speed be greater than, equal to, or less than 20 m/s?

b. Does the speed change if air resistance is a factor?

To determine

Whether the catching speed would be same as $20\frac{\text{m}}{\text{s}}$ or not.

Answer to Problem 12A

The catching speed will be same as $20\frac{\text{m}}{\text{s}}$ .

Explanation of Solution

Given:

Acceleration $=a=9.8\frac{\text{m}}{{\text{s}}^2}$

Initial speed $=v_o=20\frac{\text{m}}{\text{s}}$

Final speed $=v_f=?$

Displacement $=\Delta x=0$

Air resistance is to be neglected.

Formula Used:

  $v_f^2=v_o^2+2a\Delta x$

  $v_f$ is the final velocity

  $v_o$ is the initial velocity

  $\Delta x$ is the vertical displacement

a is the acceleration.

Calculation:

Using the kinematics equation

  $\begin{array}{l}{v}_f^2=v_o^2+2a\Delta x\\ v_f^2={20}^2+2(9.8)(0)\\ v_f=20\frac{\text{m}}{\text{s}}\end{array}$

Conclusion:

Hence, the catching speed comes out to be $20\frac{\text{m}}{\text{s}}$ .

To determine

Change in speed when air resistance is present.

Answer to Problem 12A

The speed would decrease.

Explanation of Solution

Introduction:

Velocity of an object decrease when acceleration acts in opposite direction of the motion of the object.

Due to the presence of air resistance, the ball experiences a resistive force in opposite direction of motion. This resistive force makes the ball go slower and hence the speed at the time of catching would be smaller.

Conclusion:

Hence, the catching speed would be smaller than 20 m/s if air resistance is present.