Chapter 12.5, Problem 57E

To determine

To find: the initial vertical and horizontal velocities.

Answer to Problem 57E

  $\begin{array}{c}{v}_y=26.79\text{ ft/s}\\ v_x=52.57\text{ ft/s}\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{c}{v}_o=59\text{ ft/s}\\ \theta =\text{63}°\end{array}$

Calculation:

Let the initial vertical velocity and initial horizontal velocity be $v_y\text{ and }{v}_x$ respectively.

The figure representing the given situation is as follows:

The initial vertical velocity can be evaluated as follows:

  $\begin{array}{c}{v}_y=v_o\cos \theta \\ =\left(59\text{ ft/s}\right)\text{cos63}°\\ =26.79\text{ ft/s}\end{array}$

The initial horizontal velocity can be evaluated as follows:

  $\begin{array}{c}{v}_x=v_o\sin \theta \\ =\left(59\text{ ft/s}\right)\text{sin63}°\\ =52.57\text{ ft/s}\end{array}$

Thus, the initial vertical velocity is 27.79 ft/s and initial horizontal velocity is 52.57 ft/s.