Chapter 8.7, Problem 6CFU

To determine

To find: the initial horizontal velocity and vertical velocity.

Answer to Problem 6CFU

  $\begin{array}{l}\left|\overrightarrow{v_x}\right|=38.16\text{ feet per second}\\ \left|\overrightarrow{v_y}\right|=23.85\text{ feet per second}\end{array}$

Explanation of Solution

Given information:

Initial velocity $\left|\overrightarrow{v}\right|=$ 45 feet per second

  $\theta =32°$

Calculation:

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

  $\begin{array}{c}\left|\overrightarrow{v_x}\right|=\left|\overrightarrow{v}\right|\cos \theta \\ =45\cos 32°\left[\text{Put the value of }\left|\overrightarrow{v}\right|\text{ and }\theta \right]\\ =38.16\text{ feet per second}\end{array}$

Thus the initial horizontal velocity is $38.16\text{ feet per second}$ .

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

  $\begin{array}{c}\left|\overrightarrow{v_y}\right|=\left|\overrightarrow{v}\right|\sin \theta \\ =45\sin 32°\left[\text{Put the value of }\left|\overrightarrow{v}\right|\text{ and }\theta \right]\\ =23.85\text{ feet per second}\end{array}$

Thus the initial vertical velocity is $23.85\text{ feet per second}$ .