Chapter A.10, Problem 112AYU

(a)

To determine

To find: The final velocity $v$ of an object that slides down a frictionless inclined plane of height $4$ feet.

Answer to Problem 112AYU

The final velocity is $v=16\text{ft}/\sec$ .

Explanation of Solution

Given:

Initial velocity is $v_0=0$

And,

  $v=\sqrt{64h+{\left(v_0\right)}^2}$

Calculation:

For height $4$ feet the final velocity is calculated as:

  $\begin{array}{c}v=\sqrt{64\times 4+{\left(0\right)}^2}\\ =16\end{array}$

Therefore, the final velocity is $v=16\text{ft}/\sec$ .

(b)

To determine

To find: The final velocity $v$ of an object that slides down a frictionless inclined plane of height $16$ feet.

Answer to Problem 112AYU

The final velocity is $v=32\text{ft}/\sec$ .

Explanation of Solution

Given:

Initial velocity is $v_0=0$

And $v=\sqrt{64h+{\left(v_0\right)}^2}$

Calculation:

For height $16$ feet the final velocity is calculated as:

  $\begin{array}{c}v=\sqrt{64\times 16+{\left(0\right)}^2}\\ =32\end{array}$

Therefore, the final velocity is $v=32\text{ft}/\sec$ .

(c)

To determine

To find: The final velocity $v$ of an object that slides down a frictionless inclined plane of height $2$ feet.

Answer to Problem 112AYU

The final velocity is $v=12\text{ft}/\sec$ .

Explanation of Solution

Given:

Initial velocity is $v_0=4\text{ft}/\sec$

And $v=\sqrt{64h+{\left(v_0\right)}^2}$

Calculation:

For height $2$ feet the final velocity is calculated as:

  $\begin{array}{c}v=\sqrt{64\times 2+{\left(4\right)}^2}\\ =\sqrt{144}\\ =12\end{array}$

Therefore, the final velocity is $v_0=4\text{ft}/\sec$ .