# Thread: Free Fall Differential Equations Problem - I am stuck

1. ## Free Fall Differential Equations Problem - I am stuck

Question:

An Object of mass 5.00 kg is given an initial downward velocity of 74.5 m/sec and then allowed to fall under the influence of gravity. Assume the force due to air resistance (in N) on this object is twice its speed. If it hits the ground in exactly 10 seconds, how many meters above the ground was the object when it was released?

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The part I am stuck in this problem is what will be the drag co-efficient? It says "Assume the force due to air resistance (in N) on this object is twice its speed." - This is the part I DO NOT understand at all!!!

2. Setting $x(t)$ the quote of the onbject the equation describing the 'fall' is...

$m\cdot x^{''} = -m\cdot g +2\cdot x^{'} \rightarrow x^{''} -\frac {2}{m}\cdot x^{'}= -g$ (1)

The (1) is a linear second order constanr coefficients DE with initial conditions $x(0)=x_{0}$ [ $x_{0}$ is unknown] and $x^{'}(0)= -v_{0}$ and can be solved in standard way. After that the computation of $x_{0}$ is comfortable...

Kind regards

$\chi$ $\sigma$

Question:

An Object of mass 5.00 kg is given an initial downward velocity of 74.5 m/sec and then allowed to fall under the influence of gravity. Assume the force due to air resistance (in N) on this object is twice its speed. If it hits the ground in exactly 10 seconds, how many meters above the ground was the object when it was released?

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The part I am stuck in this problem is what will be the drag co-efficient? It says "Assume the force due to air resistance (in N) on this object is twice its speed." - This is the part I DO NOT understand at all!!!
Are you serious? "Twice" means "multiply by 2"! The air resistance force is -2v. The total force, then, is -mg- 2v, due to gravity and air resistance.
$m\frac{dv}{dt}= -mg- 2v$ with v(0)= -74.5. You should be able to solve that equation for v(t). Integrating that will give x(t), the height at time t, with, of course, a constant of integration. Use the fact that x(10)= 0 to find that constant and then find x(0), the initial height.