A skydiver weighing 180lbs (including equipment) falls vertically downward from an altitude of 5000 ft and opens the parachute a
fter 10 s of free fall. Assume that the force of air resistance, which is directed opposite to the velocity, is of magnitude.75|v| when the parachute is closed and is of magnitude 12|v| when the parachute is open, where velocity v is measured in ft/s. Find the speed of the skydiver when the parachute opens.
<span>For the
presented problem, the solution would be</span><span> </span><span>v</span><span>(0)=0</span><span>v(0)=0</span><span> is</span><span>v</span><span>(</span><span>t</span><span>)−</span><span>mgb</span><span>=</span><span>e</span><span>−</span><span>b</span><span>/</span><span>m</span><span>⋅</span><span>t</span><span>(</span><span>v</span><span>0</span><span>−</span><span>mgb</span><span>)</span><span>⟺</span><span>v</span><span>(</span><span>t</span><span>)=</span><span>mgb</span><span>(</span><span>1−</span><span>e</span><span>−</span><span>b</span><span>/</span><span>m</span><span>⋅</span><span>t</span><span>)</span><span>≈</span><span>g</span><span>⋅</span><span>t</span><span>−</span><span>gb</span><span>2</span><span>m</span><span>⋅</span><span>t</span><span>2</span><span>,
with the following given, </span><span>
m</span><span>=180[lb]=81.6[kg]</span><span> </span>
<span>The solution that the
friction provides is </span><span>v</span><span>(</span><span>t</span><span>)=3501.7[m/s]</span><span>⋅</span><span>(</span><span>1−</span><span>e</span><span>−0.00280[1/s]</span><span>⋅</span><span>t</span><span>), where I get </span><span><span>96.69</span></span><span /><span><span><span><span>[</span></span><span /><span><span>m</span></span><span /><span><span><span><span>/</span></span></span></span></span><span><span><span>s</span></span><span /><span><span>]</span></span></span><span>=</span></span><span /><span><span>317.2</span></span><span /><span><span><span><span>[</span></span><span /><span><span>f</span><span>t</span></span><span /><span><span><span><span>/</span></span></span></span></span><span><span><span>s</span></span><span /><span><span>]</span></span></span></span><span><span /></span><span>. I
am hoping that this answer has satisfied your query about this specific
question.<span /></span>
As x approaches 3 from the right, the limit is 3. There is a closed hole up there AT x=3 y=7, but we don't care about what happens AT x=3, only what happens as x APPROACHES 3.
