Question: A 5000-kg elephant on friction-less skates is going 25 m/s when it gets to the bottom of a hill and arrives on level ground. Once on level ground a rocket attached to the elephant turns on generating a 8000 n thrust in the opposite direction of the elephants travel.
The left of the picture shows the body as it travels down the hill with the rocket off.
The right side of the picture shows the elephant with the rocket already activated. The rocket loses weight at a rate of 20 kg/s.
We solved this problem Mathematically and numerically.
Mathematically:
With the given information we were able to find Acceleration as a function of time by manipulating F=Ma into a(t)=F/M. The actual equation is shown on the left.
In order to find Position as a function of time we had to integrate a(t). Luckily professor Wolf was nice enough to integrate the problem for us.
The equation to the left is the position as a function of time after it was integrated by professor Wolf.
W found out that it takes the elephant traveled for 19.69075 seconds before stopping.
We plug in the time into the equation above and we found out that the elephant traveled 248.7 meters before coming to a stop.
Numerically:
Another approach we took to solve the problem was a numerically approach by using excel.
We plugged in our numbers into excel and we let it solve it numerically.
These are two copies of our excel files.
t= time
a= acceleration
Delta V= Change in velocity
V= Velocity
V_ave= Average velocity
Delta-x= Change in X
X= Position
The copy to the left shows a velocity of 0 m/s at t= 19.69, The position at this time is
248.698165 m.
In conclusion our analytically and numerically answers both match.
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