Chapter 3, Problem 21P

To determine

The initial speed of the ball.

Answer to Problem 21P

8 m/s

Explanation of Solution

Given:

The building is 45m tall and ball lands 24m from the base.

Formula Used:

The kinematics equations are:

  $\begin{array}{l}{S}_y=u_{y}t+\frac{1}{2}a{t}^2\\ u_x=S_x/t\end{array}$

Calculation:

Initial velocity along y axis

  $u_y=0\text{m/s}$

Vertical displacement

  $S_y=-45\text{ m}$

Horizontal displacement

  $S_r=-24\text{ m}$

Acceleration due to gravity

  $g=-10{\text{ m/s}}^2$

Substituting the values, to find the time.

  $\begin{array}{l}-45=0-\frac{1}{2}10t^2\\ t^2=\frac{90}{10}\\ t^2=9\\ t=3\sec \end{array}$

Substituting the values, to find the velocity.

  $\begin{array}{l}{u}_x=\frac{24}{3}\\ u_x=8\text{ m/s}\end{array}$

Conclusion:

Thus, the initial speed of ball is 8 m/s.