Chapter 3, Problem 72A

(a)

To determine

The velocity of the stone after $8.\text{0 s}$ .

Answer to Problem 72A

  $78.4\text{m/s}$

Explanation of Solution

Given:

A stone that starts from rest is in a free fall for $8.\text{0 s}$ .

Formula used:

Final velocity with constant acceleration can be obtained by,

  $v_f=v_i+a\Delta t$

Where, $v_f$ is the final velocity, $v_i$ is the initial velocity, a is the acceleration and $\Delta t$ is the time taken.

Calculation:

Since, the stone starts from rest, thus its initial velocity will be 0, that is,

  $v_i=0$

Acceleration acting on it will be due to gravity only. Thus,

  $a=9.8{\text{m/s}}^{\text{2}}$

Then, using the above mentioned formula for the final velocity,

  $\begin{array}{c}{v}_f=v_i+a\Delta t\\ =0+\left(9.8\times 8.0\right)\\ =78.4\text{m/s}\end{array}$

Conclusion:

Thus, the final velocity of the stone after $8.\text{0 s}$ is $78.4\text{m/s}$ .

(b)

To determine

The displacement of the stone in $8.\text{0 s}$ .

Answer to Problem 72A

  $313.6\text{m}$

Explanation of Solution

Given:

A stone that starts from rest is in a free fall for $8.\text{0 s}$ .

Formula used:

The distance traveled by an object with a constant acceleration can be obtained by:

  $d_f=d_i+v_i\Delta t+\frac{1}{2}a{\left(\Delta t\right)}^2$

Here, d represents displacement, v represents velocity, t represents time and a is the acceleration.

Calculation:

Since, the stone starts from rest, thus its initial velocity will be 0, that is,

  $v_i=0$

Acceleration acting on it will be due to gravity only. Thus,

  $a=9.8{\text{m/s}}^{\text{2}}$

Then, using the above-mentioned formula for the displacement of the stone in $8.\text{0 s}$ ,

  $\begin{array}{c}{d}_f=d_i+v_i\Delta t+\frac{1}{2}a{\left(\Delta t\right)}^2\\ =0+0\left(8\right)+\frac{1}{2}\left(9.8\right){\left(8.0\right)}^2\\ =313.6\text{m}\end{array}$

Conclusion:

Thus, the displacement of the stone in 8.0s is $313.6\text{m}$ .