Chapter 3.3, Problem 48SSC

To determine

The final velocity of the object.

Answer to Problem 48SSC

  $v=9.18\text{m}\cdot {\text{s}}^{\text{-1}}$

Explanation of Solution

Given:

Vertical displacement of the house keys, $h=4.3\text{m}$

Formula Used:

Third equation of motion:

  $v^2=u^2+2gh$

Where,

v is the final velocity

u is the initial velocity which is zero in this case as the object is dropped.

g is the acceleration due to gravity

  $g=9.\text{8}\text{m}\cdot {\text{s}}^{\text{-2}}$

h is the given vertical displacement.

Calculation:

Substitute the values and solve:

  $\begin{array}{l}{v}^2=0+2(9.8)(4.3)\\ v^2=84.28\\ v=9.18\text{m}\cdot {\text{s}}^{\text{-1}}\end{array}$

Conclusion:

The final velocity of the keys when they are caught is $9.18\text{m}\cdot {\text{s}}^{\text{-1}}$ .