# Problem: A girl of mass m1=60 kilograms springs from a trampoline with an initial upward velocity of v1 = 8.0 meters per second. At height h =2.0 meters above the trampoline, the girl grabs a box of mass m2 = 15 kilograms.For this problem, use g = 9.8 meters per second for the magnitude of the acceleration due to gravity.a)What is the speed of the girl immediately before she grabs the box?b)What is the speed of the girl immediately after she grabs the box?c)What is the maximum height that the girl (with box) reaches? Measure with respect to the top of the trampoline

###### FREE Expert Solution

Law of conservation of energy:

$\overline{){{\mathbf{K}}}_{{\mathbf{i}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{i}}}{\mathbf{=}}{{\mathbf{K}}}_{{\mathbf{f}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{f}}}}$

K = (1/2)mv2 and U = mgh

Law of conservation of momentum:

$\overline{)\begin{array}{rcl}{\mathbf{p}}_{\mathbf{i}}& {\mathbf{=}}& {\mathbf{p}}_{\mathbf{f}}\\ {\mathbf{p}}& {\mathbf{=}}& \mathbf{m}\mathbf{v}\end{array}}$

a)

Let  v2 be the speed of the girl before immediately before she grabs the box.

From the law of conservation of energy:

$\begin{array}{rcl}\frac{\mathbf{1}}{\mathbf{2}}\overline{){\mathbf{m}}_{\mathbf{1}}}{{\mathbf{v}}_{\mathbf{1}}}^{\mathbf{2}}\mathbf{+}\mathbf{0}& \mathbf{=}& \frac{\mathbf{1}}{\mathbf{2}}\overline{){\mathbf{m}}_{\mathbf{1}}}{{\mathbf{v}}_{\mathbf{2}}}^{\mathbf{2}}\mathbf{+}\overline{){\mathbf{m}}_{\mathbf{1}}}\mathbf{g}\mathbf{h}\\ {{\mathbf{v}}_{\mathbf{1}}}^{\mathbf{2}}& \mathbf{=}& {{\mathbf{v}}_{\mathbf{2}}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathbf{g}\mathbf{h}\\ {\mathbf{v}}_{\mathbf{2}}& \mathbf{=}& \sqrt{{{\mathbf{v}}_{\mathbf{1}}}^{\mathbf{2}}\mathbf{-}\mathbf{2}\mathbf{g}\mathbf{h}}\\ & \mathbf{=}& \sqrt{\mathbf{8}\mathbf{.}{\mathbf{0}}^{\mathbf{2}}\mathbf{-}\mathbf{\left(}\mathbf{2}\mathbf{\right)}\mathbf{\left(}\mathbf{9}\mathbf{.}\mathbf{81}\mathbf{\right)}\mathbf{\left(}\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{\right)}}\end{array}$

###### Problem Details

A girl of mass m1=60 kilograms springs from a trampoline with an initial upward velocity of v= 8.0 meters per second. At height h =2.0 meters above the trampoline, the girl grabs a box of mass m= 15 kilograms.
For this problem, use g = 9.8 meters per second for the magnitude of the acceleration due to gravity.

a)What is the speed of the girl immediately before she grabs the box?
b)What is the speed of the girl immediately after she grabs the box?
c)What is the maximum height that the girl (with box) reaches? Measure with respect to the top of the trampoline