Chapter 8, Problem 52SGA

To determine

To find: the initial horizontal velocity and vertical velocity of a soccer ball.

Answer to Problem 52SGA

  $\begin{array}{l}\left|\overrightarrow{v_x}\right|=15.9\text{ meters per second}\\ \left|\overrightarrow{v_y}\right|=8.45\text{ meters per second}\end{array}$

Explanation of Solution

Given information:

Initial velocity $\left|\overrightarrow{v}\right|=$ 18 meters per second

  $\theta =28°$

Calculation:

The initial horizontal velocity $\left|\overrightarrow{v_x}\right|$ is evaluated as follows:

  $\begin{array}{c}\left|\overrightarrow{v_x}\right|=\left|\overrightarrow{v}\right|\cos \theta \\ =18\cos 28°\left[\text{Put the value of }\left|\overrightarrow{v}\right|\text{ and }\theta \right]\\ =15.9\text{ meters per second}\end{array}$

Thus the initial horizontal velocity is $15.9\text{ meters per second}$ .

The initial vertical velocity $\left|\overrightarrow{v_y}\right|$ is evaluated as follows:

  $\begin{array}{c}\left|\overrightarrow{v_y}\right|=\left|\overrightarrow{v}\right|\sin \theta \\ =18\sin 28°\left[\text{Put the value of }\left|\overrightarrow{v}\right|\text{ and }\theta \right]\\ =8.45\text{ meters per second}\end{array}$

Thus the initial vertical velocity is $8.45\text{ meters per second}$ .