Vertical Motion and Free Fall Video Lessons

Concept

# Problem: A helicopter is ascending vertically with a speed of 5.40 m/s. At a height of 105 m above the Earth, a package is dropped from the helicopter. How much time does it take for the package to reach the ground? [Hint: What is the v0 for the package?]

###### FREE Expert Solution

Use the kinematic equation:

$\overline{){\mathbf{∆}}{\mathbf{y}}{\mathbf{=}}{{\mathbf{v}}}_{{\mathbf{0}}}{\mathbf{t}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{g}}{{\mathbf{t}}}^{{\mathbf{2}}}}$

Solve, substitute, and calculate t as follows:

$\begin{array}{rcl}\mathbf{105}& \mathbf{=}& \mathbf{\left(}\mathbf{-}\mathbf{5}\mathbf{.}\mathbf{40}\mathbf{\right)}\mathbf{t}\mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\left(}\mathbf{9}\mathbf{.}\mathbf{81}\mathbf{\right)}{\mathbf{t}}^{\mathbf{2}}\\ \mathbf{4}\mathbf{.}\mathbf{905}{\mathbf{t}}^{\mathbf{2}}\mathbf{-}\mathbf{5}\mathbf{.}\mathbf{40}\mathbf{t}\mathbf{-}\mathbf{105}& \mathbf{=}& \mathbf{0}\end{array}$

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###### Problem Details

A helicopter is ascending vertically with a speed of 5.40 m/s. At a height of 105 m above the Earth, a package is dropped from the helicopter. How much time does it take for the package to reach the ground? [Hint: What is the v0 for the package?]