Chapter 13.1, Problem 60E

To determine

To calculate: The initial vertical and horizontal velocities of the rock.

Answer to Problem 60E

The initial vertical velocity is $19.8$feet per second and initial horizontal velocity is $19.8$feet per second.

Explanation of Solution

Given information:

The initial velocity with which a rock is thrown is 28 feet per second at angle of $45°$ with horizontal.

Formula used:

The initial horizontal velocity is $v_x=v\cos \theta$ and initial vertical velocity $v_y=v\sin \theta$ where v is the initial velocity with which object is thrown and $\theta$ is the angle it makes with the horizontal.

Calculation:

Consider the provided information that initial velocity with which a rock is thrown is 28 feet per second at angle of $45°$ with horizontal.

Recall that the initial horizontal velocity is $v_x=v\cos \theta$ and initial vertical velocity $v_y=v\sin \theta$ where v is the initial velocity with which object is thrown and $\theta$ is the angle it makes with the horizontal.

Here, $v=28$ and $\theta =45°$ .

Therefore, initial horizontal velocity is,

  $\begin{array}{c}{v}_x=v\cos \theta \\ v_x=28\cos 45°\\ v_x=\frac{28}{\sqrt{2}}\\ v_x=19.8\end{array}$

And, initial vertical velocity is,

  $\begin{array}{c}{v}_y=v\sin \theta \\ v_y=28\cos 45°\\ v_y=\frac{28}{\sqrt{2}}\\ v_y=19.8\end{array}$

Thus, the initial vertical velocity is $19.8$ feet per second and initial horizontal velocity is $19.8$ feet per second.