# Physics Topics: Vertical Motion with Constant Acceleration

Suppose a frog gets launched vertically into the air as this frog did during the launch of NASA's LADEE (Lunar Atmosphere and Dust Environment Explorer) spacecraft:

A NASA scientist gives you the task of calculating the frog's initial launch velocity provided by the spacecraft blast.  You only know one piece of information: the frog reaches a maximum height of 100m.  What do you do?  Assuming the frog's motion is perfectly vertical (unrealistic, but let's go with it), you could use one of the many kinematic equations for one dimensional motion with constant acceleration:

xf-xi=(1/2)(vf+vi)t
vf=vi+at
xf-xi=vi+(1/2)at2
vf2=vi2+2a(xf-xi)

But which one to use?  We know xf-xi=100m.  We also know that when the frog reaches his maximum height, he has a final velocity of zero, vf=0.  Additionally, we know that once the frog leaves the ground, he has a constant acceleration of a=g=-9.81 m/s2.  Now, look back at the four equations above.  We want to pick the equation where all the values are known except vi... Looks like we want to use the last equation listed above.

So, let's solve for the frog's initial velocity:
vf2=vi2+2a(xf-xi)
0=vi2+2g(xf-xi)
vi2=-2g(xf-xi)
vi=sqrt[-2g(xf-xi)]
vi=sqrt(-2*-9.81*100)
vi=44.3 m/s

Hopefully he survived! Poor guy.

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Maria W.

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